Answer:pl z give me brainliest the crown next to the stars when two people answer :) have a good day ;)
Step-by-step explanation:
hope this helped
Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 and 3.5 mpg, respectively. Use Table 1.
a. What is the probability that a randomly selected passenger car gets more than 35 mpg?
b. What is the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg?
c. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 35 mpg?
the probability that a randomly selected passenger car gets more than 35 mpg is approximately 0.3665.
the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg is approximately 0.087
the probability that all of the passenger cars get more than 35 mpg is approximately 0.015.
We need to find [tex]P(X > 35),[/tex] where X is the mpg rating of a randomly selected passenger car.
The standard normal distribution and Table 1, we have:
[tex]z = (35 - 33.8) / 3.5 = 0.34[/tex]
[tex]P(X > 35) = P(Z > 0.34) = 0.3665[/tex]
[tex]P(\bar X > 35)[/tex], were [tex]\bar X[/tex] is the sample mean mpg rating of four randomly selected passenger cars.
The population standard deviation, we use the t-distribution with [tex]n-1[/tex] degrees of freedom (were [tex]n = 4[/tex]) and Table 1. We have:
[tex]t = (35 - 33.8) / (3.5 / \sqrt(4)) = 1.83[/tex]
Using Table 1 with 3 degrees of freedom ([tex]n-1 = 4-1[/tex]), we find:
[tex]P(T > 1.83) = 0.087[/tex]
We need to find [tex]P(X1 > 35[/tex] and [tex]X2 > 35[/tex] and [tex]X3 > 35[/tex] and [tex]X4 > 35[/tex]), where X1, X2, X3, and X4 are the mpg ratings of four randomly selected passenger cars.
Since the mpg ratings of the four cars are independent and identically distributed, we have:
[tex]P(X1 > 35[/tex]and[tex]X2 > 35[/tex] and [tex]X3 > 35[/tex] and [tex]X4 > 35[/tex]) =[tex]P(X > 35)^4[/tex]
From part (a), we know that[tex]P(X > 35) = 0.3665.[/tex]
[tex]P(X1 > 35[/tex]and [tex]X2 > 35[/tex] and[tex]X3 > 35[/tex] and [tex]X4 > 35) = 0.3665^4 \approx 0.015[/tex]
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Evaluate the following. Write an exponential function of the form y=ab^x that has the given points 1. (1,5), (2, 7)
Answer:
Step-by-step explanation:
25
=
a
b
−
2
10
=
a
b
1
A woman at a point A on the shore of a circular lake with radius 4 wants to arrive at the point C diametrically opposite to A on the other side of the lake in the shortest possible time. She can walk at the rate of 10 miles and row a boat at 5 miles
Answer: To minimize the time taken by the woman to reach point C, she should minimize the total distance traveled, which is the sum of the distance she walks and the distance she rows.
Let's call point B the point where the woman switches from walking to rowing. We can find the location of point B by drawing a straight line from A to the center of the lake, and then continuing that line on the other side of the lake to point C. Point B is the point where this line intersects the circle of the lake.
Since the radius of the lake is 4, the distance from A to the center of the lake is also 4. Therefore, the distance from A to B is also 4. The distance from B to C is also 4, since C is diametrically opposite to A.
Let's call the distance that the woman rows from B to C d. Then the distance that she walks from A to B is 4 - d.
The time taken to walk a distance of (4 - d) miles is:
t1 = (4 - d) / 10
The time taken to row a distance of d miles is:
t2 = d / 5
The total time taken is:
T = t1 + t2 = (4 - d) / 10 + d / 5
Simplifying, we get:
T = (8 + d) / 20
To minimize T, we need to find the value of d that minimizes (8 + d) / 20. We can do this by taking the derivative of (8 + d) / 20 with respect to d and setting it to 0:
d(T) / d(d) = 1/20
Setting this to 0, we get:
1/20 = 0
This is obviously not true, so there is no minimum value of T. However, we can see that as d gets larger, T gets larger, and as d gets smaller, T gets smaller. Therefore, the minimum value of T occurs at one of the endpoints of the interval [0, 4]. Since d cannot be negative, the only endpoint we need to consider is d = 4.
When d = 4, the woman rows the entire distance from B to C, and does not need to walk at all. Therefore, the total time taken is:
T = (8 + 4) / 20 = 0.6 hours
Therefore, the woman should walk to point B, and then row the rest of the way to point C, to arrive in the shortest possible time.
Step-by-step explanation:
in a survey of 300 college graduates, 53% reported that they entered a profession closely related to their college major. if 9 of those survey subjects are randomly selected with replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major? round to four decimal places.
The probability that 3 of the 9 randomly selected subjects entered a profession closely related to their college major is approximately 0.1665, or 16.65%.
To find the probability that 3 out of 9 randomly selected subjects entered a profession closely related to their college major, we can use the binomial probability formula:
[tex]P(X = k) = (n choose k) * p^k * (1 - p)^{n - k}[/tex]
where:
- P(X = k) is the probability of k successes (in this case, 3 people entering a profession closely related to their major)
- n is the number of trials (9 subjects)
- k is the number of successes (3 people)
- p is the probability of success (53% or 0.53)
- (n choose k) is the number of combinations of n items taken k at a time, which can be calculated as C(n, k) = n! / (k! * (n - k)!)
Plugging in the values, we get:
[tex]P(X = 3) = C(9, 3) * (0.53)^3 * (1 - 0.53)^{9 - 3}[/tex]
First, calculate the combinations (n choose k):
C(9, 3) = 9! / (3! * (9 - 3)!)
C(9, 3) = 9! / (3! * 6!)
C(9, 3) = 362880 / (6 * 720)
C(9, 3) = 84
Now, calculate the probabilities:
[tex]P(X = 3) = 84 * (0.53)^3 * (0.47)^6[/tex]
P(X = 3) = 84 * 0.148877 * 0.013325
P(X = 3) ≈ 0.1665.
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A silver picture frame has a mass of 100grams and a volume of 10cubic centimeters. What is its density?
Math is NOT my strong suit :)
Thus, the density of the silver picture frame is found to be 10 grams / cubic centimeters.
Explain about the density:We use the word "density" to indicate how much space (or "volume") an object or substance occupies in relation to the total quantity of matter contained therein (its mass).
Density can also be defined as the quantity of mass per unit of volume. A dense object is one that is both hefty and small. An object has a low density if it is light and occupies a large amount of space.
Density = mass / volume
given data:
mass of the silver picture frame = 100 grams
Volume = 10 cubic centimetres
Density = mass / volume
Density = 100 grams/ 10 cubic centimeters
Density = 10 grams / cubic centimeters
Thus, the density of the silver picture frame is found to be 10 grams / cubic centimeters.
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what is the answer of this question (please i need help)
Answer:
The answer is B ([tex]x=\frac{6}{5}[/tex])
Step-by-step explanation:
We start with creating labels for the shapes that represent what they value -at first I tried multiplying the 5x by 4 but there wasn't an answer for that.
[tex]5x+4=10[/tex]
First we just simplify,
[tex]5x (-4)=10(-4)[/tex]
[tex]5x=6[/tex]
then divide,
[tex]\frac{5x}{5} =\frac{6}{5}[/tex]
and we end up with:
[tex]x=\frac{6}{5}[/tex]
or
B
PLEASE HELP. Lesson 15.3 Tangents and Circumscribed Angles
Proof of Circumscribed Angle Theorem
Given: ZAXB is a circumscribed angle of circle C.
Prove: ZAXB and ZACB are supplementary.
Complete the proof.
A
B
C
If ZAXB is a circumscribed angle of circle C, XA and XB are
Select an answer to the circle
The assumption that AXB is a bounded angle is false, as a result, if AXB is a circumscribed angle of circle C, then AXB and ACB are supplementary.
How to prove circumscribed angles?To complete the proof of the Circumscribed Angle Theorem, use the fact that an inscribed angle of a circle is equal to half of the central angle that intercepts the same arc.
Since angle ∠AXB is circumscribed by the circle, point X lies on the circumference of the circle. Therefore, angles ∠CXA and ∠CXB are inscribed angles that intercept the same arc AB.
By the Inscribed Angle Theorem:
∠CXA = ½∠CAB
∠CXB = ½∠CAB
Adding these two equations:
∠CXA + ∠CXB = ½∠CAB + ½∠CAB
∠CXA + ∠CXB = ∠CAB
Now, observe that angles ∠CAB and ∠ACB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠CAB + ∠ACB = 180°
Substituting ∠CAB with ∠CXA + ∠CXB:
∠CXA + ∠CXB + ∠ACB = 180°
Finally, ∠AXB and ∠CXB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠AXB + ∠CXB = 180°
Substituting ∠CXB with ∠CAB - ∠CXA:
∠AXB + ∠CAB - ∠CXA = 180°
Adding ∠CXA to both sides:
∠AXB + ∠CAB = ∠ACB + 180°
Substituting ∠AXB + ∠CAB with 180° (since they are adjacent angles that together make a straight line):
180° = ∠ACB + 180°
Simplifying:
∠ACB = 0°
This is a contradiction, since we know that ∠ACB is a non-zero angle. Therefore, our assumption that ∠AXB is a circumscribed angle must be false. Hence, we have proved that if ∠AXB is a circumscribed angle of circle C, then ∠AXB and ∠ACB are supplementary.
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tarting in the 1970s, medical technology allowed babies with very low birth weight (vlbw, less than 1500 grams, or about 3.3 pounds) to survive without major handicaps. it was noticed that these children nonetheless had difficulties in school and as adults. a long study has followed 242 randomly selected vlbw babies to age 20 years, along with a control group of 233 randomly selected babies from the same population who had normal birth weight.49 (a) is this an experiment or an observational study? why? (b) at age 20, 179 of the vlbw group and 193 of the control group had graduated from high school. is the graduation rate among the vlbw group significantly lower than for the normal-birth-weight controls? give appropriate statistical evidence to justify your answer. ap3.33 a nuclear power plant
(a) This is an observational study.
The reason is that the researchers did not manipulate any variables or conditions; they simply observed and collected data on the two groups of babies (VLBW and normal birth weight) as they grew up.
(b) The p-value (0.0013) is less than the significance level (typically 0.05), we reject the null hypothesis.
There is sufficient evidence to suggest that the graduation rate among the VLBW group is significantly lower than the normal-birth-weight controls.
To determine if the graduation rate among the VLBW group is significantly lower than the normal-birth-weight controls, we can perform a hypothesis test using the proportion of high school graduates in each group.
State the null and alternative hypotheses.
Null hypothesis (H0):
There is no significant difference in graduation rates between the VLBW group and the control group ([tex]p_VLBW = p_control).[/tex]
Alternative hypothesis (Ha):
The graduation rate among the VLBW group is significantly lower than the control group [tex](p_VLBW < p_control).[/tex].
Calculate the sample proportions and the pooled proportion.
[tex]p_VLBW[/tex] = 179/242 = 0.7397
[tex]p_control = 193/233 = 0.8283.[/tex]
[tex]p_pooled = (179 + 193) / (242 + 233) = 0.7842[/tex]
Calculate the test statistic.
[tex]z = (p_VLBW - p_control) / sqrt(p_pooled * (1 - p_pooled) * (1/242 + 1/233)) = -3.0074[/tex]
Determine the p-value.
Using a z-table or calculator, the p-value for z = -3.0074 is approximately 0.0013.
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Write a rule for the n th term of the sequence for which a az = 3 and r = 13.0
The rule for the nth term of the sequence is: an = [tex]3 * 13.0^(n-1)[/tex]
What is arithmetic progression ?An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
The rule for the nth term of a geometric sequence is given by:
an = a1 * rn-1
where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio of the sequence
n = the position of the term in the sequence
Using the given values, we can write the rule for the nth term of the sequence as:
an =[tex]a * r^(n-1)[/tex]
where:
a = 3 (given)
r = 13.0 (given)
Therefore, the rule for the nth term of the sequence is:
an =[tex]3 * 13.0^(n-1)[/tex]
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In January the total cost for 275 minutes was $ 55.5 while I’m February , the total cost for 225 minutes was $54.5 the constant charge for each minute used is
Answer:
[tex]\frac{1}{50}[/tex]
Step-by-step explanation:
[tex]\frac{54.5-55.5}{225-275}[/tex] = [tex]\frac{-1}{-50}[/tex] = [tex]\frac{1}{50}[/tex]
Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her
car.
We can use the equation y = 38.8x to find how many miles Camila can drive her car for each gallon of gas, and then use that information to find how many gallons of gas she would need to drive the same distance as Julieta.
Julieta drives 333 miles using 10 gallons of gas, so her car can travel 333/10 = 33.3 miles per gallon.
To find how many miles Camila's car can travel per gallon, we can use the equation y = 38.8x, where x is the number of gallons of gas. If Camila uses 1 gallon of gas, then y = 38.8(1) = 38.8 miles. Therefore, Camila's car can travel 38.8 miles per gallon.
To travel 333 miles like Julieta, Camila would need to use:
333 miles / 38.8 miles per gallon = 8.58 gallons of gas
Therefore, Camila would need to use 8.58 gallons of gas to travel the same distance as Julieta.
mrs. blue wants her students to be able to write two column geometric proofs. which is the most appropriate way to determine their mastery?
In ΔDEF, DM is a median, M ∈ EF, and DM = EF. DL is an angle bisector of ∠EDF, L ∈ EF, and m∠DLF = 64°. Find the measure of the smallest angle of ΔDEF.
the measure of the smallest angle of ΔDEF is approximately 41.41°.
How to solve the question?
In ΔDEF, DM is a median and M is on EF. Additionally, DM = EF, and DL is an angle bisector of ∠EDF, L is on EF, and m∠DLF = 64°. We need to find the measure of the smallest angle of ΔDEF.
Since DM is a median, it divides EF into two equal parts, EM and MF. Thus, EM = MF = DM/2 = EF/2.
Let x be the measure of ∠EDF. Then, we know that ∠EDM = ∠FDM = 90° because DM is a median.
Using the angle bisector theorem, we know that DL/EL = DF/EF. Since DL is an angle bisector, we also know that ∠DLE = ∠ELF = x/2. Therefore, we have:
DL/EL = DF/EF
DL/(EF/2) = DF/EF
DL = DF/2
Now, we can use the Law of Cosines in ΔDEF to find DF in terms of x:
DF² = DE² + EF² - 2(DE)(EF)cos(x)
DF² = DM² + MF² - 2(DM)(MF)cos(x)
DF² = (EF)²/4 + (EF)²/4 - (EF)²cos(x)
DF² = (EF)²/2 - (EF)²cos(x)
Since DL = DF/2, we have:
DL² = (EF)²/8 - (EF)²cos(x)/4
Using the angle bisector theorem again, we know that EL/FL = DE/DF. Since DL = DF/2, we also know that FL = EF - DL = EF/2. Therefore, we have:
EL/EF - EL/2 = DE/DF
EL/EF - EL/(2DL) = DE/DF
EL/EF - EL/(EF/4) = DE/DF
EL = EF(DE/DF)/3
Now, we can use the Law of Cosines again in ΔDEL to find DE in terms of x:
DE² = DL²+ EL² - 2(DL)(EL)cos(x/2)
DE² = (EF)²/8 - (EF)^2cos(x)/4 + [EF(DE/DF)/3]² - 2(DL)(EF(DE/DF)/3)cos(x/2)
DE² = (EF)²/8 - (EF)^2cos(x)/4 + (EF)²(DE/DF)^2/9 - (EF)(DE/DF)(EF/6)cos(x/2)
Since DM = EF, we have DE = DM - EM = EF/2 - EF/4 = EF/4. Thus, we can substitute this into the equation above and simplify:
(EF/4)²= (EF)²/8 - (EF)^2cos(x)/4 + (EF)^2(DE/DF)²/9 - (EF)(DE/DF)(EF/6)cos(x/2)
(EF)²/16 = (EF)²/8 - (EF)²cos(x)/4 + (EF)²(DE/DF)²/9 - (EF)(DE/DF)(EF/6)cos(x/2)
0 = (EF)²/72 - (EF)²cos(x)/4 + (EF)²(DE/DF)²/9 - (EF)(DE/DF)(EF/6)cos(x/2)
Now, we can substitute DL = DF/2 = (EF/4)/2 = EF/8 and EL = EF(DE/DF)/3 = EF(DE)/(3EF/4) = 4DE/3 into the equation above and simplify:
0 = (EF)²/72 - (EF)²cos(x)/4 + (EF)²(DE/DF)²/9 - (EF)(DE/DF)(EF/6)cos(x/2)
0 = (EF)²/72 - (EF)²cos(x)/4 + (EF)^2(DE/DF)²/9 - (EF/8)(4DE/3)(EF/6)cos(x/2)
0 = (EF)²/72 - (EF)²cos(x)/4 + (EF)²(DE/DF)²/9 - (EF²/72)cos(x/2)
0 = (EF)²/72 - (EF)²cos(x)/4 + (EF)²(DE/DF)²/9 - (EF)²cos(x/2)/18
Simplifying this equation, we get:
cos(x)/4 - cos(x/2)/18 = (EF)²/72 - (EF)²(DE/DF)²/9
Now, we can substitute DE = EF/4 and DF = EF/2 into the equation above and simplify:
cos(x)/4 - cos(x/2)/18 = (EF)²/72 - (EF)²/144
cos(x)/4 - cos(x/2)/18 = (EF)²/144
We know that cos(x) is negative because x is the measure of the smallest angle of ΔDEF, so we can take the absolute value of both sides of the equation:
|cos(x)/4 - cos(x/2)/18| = (EF)²/144
Since 0° < x < 180°, we know that cos(x/2) > cos(x), so we can simplify further:
cos(x/2)/18 - cos(x)/4 = (EF)²/144
Now, we can substitute the given value of ∠DLF = 64° into the equation above and solve for EF:
cos(32°)/18 - cos(128°)/4 = (EF)^2/144
0.0289 - (-0.2113) = (EF)²/144
0.2402 = (EF)²/144
EF = √(0.2402*144)
EF ≈ 4.8044
Finally, we can use the Law of Cosines in ΔDEF to find x:
cos(x) = (DE² + EF² - DF²)/(2(DE)(EF))
cos(x) = (EF²/16 + EF² - EF²/4)/(2(EF/4)(EF))
cos(x) = 3/4
x = arccos(3/4)
x ≈ 41.41°
Therefore, the measure of the smallest angle of ΔDEF is approximately 41.41°.
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Use the law of sines to find the indicated side x. ( Assume a=160). Round answer to one decimal place. A= 102, B =28
Using the law of sines, the value of the indicated side x, is calculated to one decimal place as: 125.3.
What is the Law of Sines?The Law of Sines is a trigonometric formula used to relate the side lengths and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be represented as:
sin A/a = sin B/b = sin C/c
Thus, we have:
C = 180 - 102 - 28 = 50°
a = 160
A = 102°
c = x = ?
Applying the law of sines, we have:
sin 102/160 = sin 50/x
Cross multiply:
x = sin 50 * 160 / sin 102
x ≈ 125.3
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patients arrive at a clinic at the rate of 90 per hour and independently of one another. four servers are employed. data analysis shows that service times at the reception counter are exponentially distributed averaging 2.4 minutes per customer. if all other m/m/s model assumptions apply (and time units are minutes) what would be the average arrival rate (lambda)?
The average arrival rate is 0.4167 customers per minute.
The average arrival rate (lambda) can be calculated using Little's Law, which states that the average number of
customers in a system (L) is equal to the average arrival rate (lambda) multiplied by the average time spent in the
system (W).
Since we know that the service times are exponentially distributed with an average of 2.4 minutes per customer, we
can use the formula for the mean of an exponential distribution, which is 1/lambda.
So, 2.4 = 1/lambda
Solving for lambda, we get lambda = 1/2.4 = 0.4167 customers per minute
Therefore, the average arrival rate is 0.4167 customers per minute.
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The volume of a box in the shape of a rectangular prism is 84 in³. The height is is 3 in. and the length is 7 in. Determine the width, in inches, of the box.
Answer:
The width is 4 inches
Step-by-step explanation:
Volume is the length x the width x height
84 = 7w3
84 = 21w Divide both sides by 21
4 = w
Helping in the name of Jesus.
You decide to invest in a period annuity that offers 4.5% APR compounded
monthly for 20 years. How much money will you need to invest if your desired
yearly income is $42,000?
OA. $553,229.03
B. $450,000.00
C. $420,000.00
D. $568,793.79
Answer: To calculate the amount of money you would need to invest in a period annuity that offers 4.5% APR compounded monthly for 20 years to receive an annual income of $42,000, you can use the following formula:
PV = A * [(1 - (1+r)^(-n)) / r]
where:
PV = present value (amount of money you need to invest)
A = annual income ($42,000 in this case)
r = interest rate per period (4.5% APR compounded monthly, or 0.045/12 = 0.00375 per month)
n = total number of periods (20 years x 12 months per year = 240 months)
Plugging in the numbers, we get:
PV = $42,000 * [(1 - (1+0.00375)^(-240)) / 0.00375]
PV = $553,229.03
Therefore, the answer is (A) $553,229.03.
Step-by-step explanation:
The total bill at the restaurant was $158.56, without tax. If tax was 6% and gratuity 15%, what was the total amount of the bill?
The total amount of the bill, including tax and gratuity, was $191.85.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
The first step is to calculate the amount of tax and the amount of gratuity:
Amount of tax = 6% of $158.56 = $9.51
Amount of gratuity = 15% of $158.56 = $23.78
Next, we add the tax and the gratuity to the original bill:
Total bill = $158.56 + $9.51 + $23.78 = $191.85
Therefore, the total amount of the bill, including tax and gratuity, was $191.85.
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The ratio of the weight to the mass is constant. Which statement describes the ratio of the weight to the mass and the value of x in the table?
The ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.
What is mass and weight?The quantity of matter in an object is measured by its mass, which is commonly expressed in kilogrammes or grammes. Since mass is a scalar quantity, the gravitational field has no effect on it. The force of gravity acting on an object is quantified by weight, which is commonly expressed in newtons or pounds. Weight is a vector quantity that is influenced by the strength of the gravitational field. While an object's mass is constant, its weight might vary depending on the gravitational field.
The ratio of weight to mass according to the given table is:
weight / mass = 196 / 20 = 98/10
The ratio is constant thus for x we have:
1078 / x = 98 / 10
Using cross multiplication we have:
x = 1078 (10) / 98 = 110
Hence, the ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.
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The complete question is:
Baseball Field Problem
Find the amount of fencing, dirt, and sod needed to rebuild the baseball field.
380 to the fence
Fencer
'Is'
Goss
Dit
Dirf
Cr=10¹
Grass
Grass
Fence
Dint
Note: Not drown to scale
S
15'
The baseball field's fence, soil and sod requirements will be-: Length of fencing ≈ 1410.5 feet, Area of the sod ≈ 118017.13 ft², Area of of the field covered with dirt ≈ 7,049.6 ft²
How to find the area of sector of Circle?To find the area of a sector of a circle:
The sector's central angle, expressed in degrees, can be measured or calculated.Calculate or measure the circle's radius (r).Use this equation: Sector area is equal to (θ/360) * r2 *.Insert the formula's values for r and θ.Apply the formula to the area to calculate it.Round the outcome to the required degree of precision.The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;
Circle's Area can be given by, (A)= π × r²
Circle's Circumference can be given by, (C) = 2 × π × r
Where, 'r' denotes the radius of the circle
The area of a quarter of a circle is therefore= A ÷ 4
The perimeter of a quarter of a circle = C ÷ 4
Taking reference from the image,
Fencing; (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15
Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5
The fencing ≈ 1410.5 feet
Grass; π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13
The area covered by the sod is about 118017.13 square feet
Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6
The area occupied by the dirt is about 7049.6 square feet
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Complete Question:Find the amount of fencing, dirt, and sod needed to rebuild the baseball field?(refer to image attached for dimensions of field)
if a person consumes 65 grams of protein and a total of 2700 kcalories per day, approximately what percentage of energy would be derived from protein?
Approximately 9.63% of the energy consumed by the person would be derived from protein.
How to calculate percentage of energy from protein?To calculate the percentage of energy derived from protein, we need to first convert the amount of protein consumed from grams to calories. Protein provides approximately 4 calories per gram. Therefore, 65 grams of protein would provide:
65 grams * 4 calories/gram = 260 calories
This gives us 260 calories from protein.
To find the percentage of energy derived from protein, we can divide the calories from protein by the total calories consumed and multiply by 100:
260 calories / 2700 calories * 100% ≈ 9.63%
Therefore, approximately 9.63% of the energy consumed by the person would be derived from protein.
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Yuto and Riko went for a bike ride on the same path. When Riko left their house, Yuto was 5.25 miles along the path. If Yuto's average speed was 0.25 miles per minute and Riko's average speed was 0.35 miles per minute, then Riko will be behind Yuto when 0
Yuto and Riko will meet 73.5 minutes after Yuto started riding, or 52.5 minutes after Riko started riding.
How to find distance when rate and time are given?
We can find the distance by following formula ,
Distance = rate × time
Let t be the time in minutes that Riko rides until she catches up with Yuto. At that time, Yuto will have also ridden for t minutes, plus the additional time it took for him to get to his starting point, which we don't know yet.
The distance Riko covers in t minutes is
distance = rate × time
distance = 0.35 miles/minute × t minutes
distance = 0.35t miles
At the time that Riko catches up with Yuto, Yuto will have ridden a total distance,
distance = rate × time + distance from starting point
distance = 0.25t + 5.25 miles
Since Riko catches up with Yuto at the same location, their distances will be equal. So we can set the two expressions for distance equal to each other,
0.35t = 0.25t + 5.25
Simplifying this equation,
0.1t = 5.25
t = 52.5 minutes
So, Riko will catch up with Yuto 52.5 minutes after she starts riding. To find out when they will meet, we can add 52.5 minutes to Yuto's starting time. Since Yuto's speed is 0.25 miles/minute, he covers 5.25 miles in
time = distance / rate
time = 5.25 miles / 0.25 miles/minute
time = 21 minutes
So Yuto started riding 21 minutes before Riko, which means they will meet,
meeting time = Riko's starting time + time to catch up
meeting time = Yuto's starting time + 52.5 minutes
meeting time = 21 minutes + 52.5 minutes
meeting time = 73.5 minutes
Therefore, Yuto and Riko will meet 73.5 minutes after Yuto started riding, or 52.5 minutes after Riko started riding.
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Correct question is "Yuto and Riko went for a bike ride on the same path. When Riko left their house, Yuto was 5.25 miles along the path. If Yuto's average speed was 0.25 miles per minute and Riko's average speed was 0.35 miles per minute, then Riko will be behind Yuto when 0 . When will they meet?"
Jack is running a 5-mile race with Jill. Jack's run is represented by the function d = 0.05t, where d is
distance traveled in miles and t is the minutes run. Jill's run is represented by d = 0.04t+ 0.5.
Part A
How do the graphs of Jack's representative function and Jill's representative function compare to the
graph of the linear parent function?
Part B
What do the effects of comparing Jack and Jill's functions to the linear parent function mean in the real-
world context?
A) Their graphs will be different from the graph of the linear parent function. B) In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends.
What is y-intercept?The y-intercept is the point where the graph of a function intersects with the y-axis. It is the point at which the value of x is 0.
According to question:Part A:
The linear parent function is represented by y = mx + b, where m is the slope and b is the y-intercept. The slope of the linear parent function is constant, while the y-intercept can vary.
In Jack's function, d = 0.05t, the slope is 0.05, which means that for every minute he runs, he travels 0.05 miles. The y-intercept is 0, which means that he starts at 0 miles.
In Jill's function, d = 0.04t + 0.5, the slope is 0.04, which means that for every minute she runs, she travels 0.04 miles. The y-intercept is 0.5, which means that she starts at 0.5 miles.
Both functions are linear, but they have different slopes and y-intercepts. Therefore, their graphs will be different from the graph of the linear parent function.
Part B:
Comparing Jack and Jill's functions to the linear parent function can give us insights into their race. The fact that their functions are linear means that they are running at a constant rate. However, the different slopes and y-intercepts mean that they are running at different rates and starting at different distances.
For example, we can see from their functions that Jack is running faster than Jill since his slope is larger. We can also see that Jill has a head start since her y-intercept is larger. By comparing their functions, we can make predictions about who will win the race or how far ahead one person will be at a certain time.
In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends. By understanding the relationship between variables, we can make informed decisions and predictions.
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Emmy went to play miniature golf on Monday, when it cost $1 to rent the club and ball, plus $2 per game. Liam went Thursday, paying $1 per game, plus rental fees of $5. By coincidence, they played the same number of games for the same total cost. How many games did each one play?
Emmy and Liam each played 4 games according to the given statement.
What is an equation?An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.
Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.
Let us suppose the number of games played = x.
Thus, for Emmy we have:
E = 1 + 2x
For Liam the equation is:
L = 5 + 1x
Equating the two equations we have:
1 + 2x = 5 + 1x
x = 4
Hence, Emmy and Liam each played 4 games according to the given statement.
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Students made a craft project at camp. They used 2 small pine cone patterns and 1 large pine cone pattern complete the table to find how many patterns were used for the different numbers of projects
There were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
When 50 students constructed one craft project each using two little pine cone patterns and one giant pine cone pattern, it is the question of how many small and large pine cone patterns were utilised overall:
We can begin by figuring out how many little pine cone patterns were utilized overall to solve this.
Since each student used 2 small pine cone patterns, we can multiply 2 by 50 (the number of students) to get:
2 x 50 = 100 small pine cone patterns used
Similarly, we can calculate the total number of large pine cone patterns used by multiplying the number of students (50) by 1 :
1 x 50 = 50 large pine cone patterns used
Therefore, in total, there were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
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--The complete Question is, If a camp has 50 students and each student made one craft project using 2 small pine cone patterns and 1 large pine cone pattern, how many small and large pine cone patterns were used in total? --
please read the phtot/picture its worth 18 ponits please help its worth 89 percent of my grade
2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.
4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.
4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
a. The diagram shows 3/5 by dividing the whole rectangle into 5 equal parts horizontally and shading 3 of those parts. This means that the shaded portion represents 3 out of 5 equal parts.
b. The diagram shows 3 * 1/5 by shading one-fifth of the rectangle, and then repeating this process three times. This means that the shaded portion represents three times one-fifth of the whole.
c. The value of 3/5 is equivalent to 0.6 or 60%. This means that if we divide a whole into 5 equal parts, and take 3 of those parts, we have 60% of the whole.
a. The expression 2(4/3) represents the shaded parts of the diagram by first finding the area of one shaded rectangle, which is 4/3. Then, we multiply this area by 2 because there are two shaded rectangles in the diagram. Therefore, 2(4/3) gives us the total shaded area.
b. The expression 4 * 2/3 represents the shaded parts of the diagram by multiplying the width of the shaded rectangle (2 units) by its height (2/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2/3 gives us the total shaded area.
c. The expression 4 * 2 * 1/3 represents the shaded parts of the diagram by multiplying the length of the shaded rectangle (4 units) by its width (2 units) by its height (1/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2 * 1/3 gives us the total shaded area.
Hence, 2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.
4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.
4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.
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You deposit $150 in an investment account that earns 6% annual interest compounded annually. You make no additional deposits or withdrawals. What is the balance of this account after 5 years
Answer:200.734
Step-by-step explanation:
150(1+0.06)^t
t=number of years
150(1.060)^5
200.73383664
round
200.734
The balance of this account after 5 years is $200.73
What is Compound interest?Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
Amount = [tex]P(1+r/n)^n^t[/tex] where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year, & t = time in years.
The given principal is $150 for 5 years & annual interest rate is 6%.
To find the amount compunded annualy at 6% for 5 years substituting the given values in the above formula i.e.
Amount = [tex]P(1+r/n)^n^t[/tex]
Amount = $[tex]150(1+0.06)^5[/tex]
Amount = $200.73
Hence, the total amount accumulated for 5 years will be $200.73
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i need help with this quick please help
Answer:
19.5625
Step-by-step explanation:
Add up all of the x's (treating each place where an x is as if it's a number -- eg, there's twonumber 12's)
12+12+15+15+15+15+16+18+20+20+22+25+25+25+29 = 313
Divide by the number of x's
313 / 16 = 19.5625
Which expression is equivalent to −3(2x − 8) + 4x? A −2x− 8 B −2x+ 24 C −10x - 8 D −10x + 24
Therefore, the expression [tex]-3(2x - 8) + 4x[/tex] is equivalent to option B, which is. [tex]-2x+24[/tex].
ExpressionTo simplify an expression, you typically want to combine like terms and perform any necessary operations in the correct order. Here are the steps you can follow:
Identify any like terms in the expression. Like terms are terms that have the same variables raised to the same powers.
Combine the coefficients of like terms. If there are no like terms, leave the expression as is.
Simplify any operations in the expression, such as multiplication, division, addition, or subtraction, according to the order of operations.
Check if the expression can be simplified further. If it can, repeat steps 1-3 until the expression cannot be simplified further.
Here's an example of how to simplify the expression. [tex]3x + 2x^2 - 5x - x^2[/tex]:
Identify like terms: 3x and -5x are like terms, as are. [tex]2x^2[/tex] and [tex]-x^2[/tex].
Combine the coefficients of like terms: [tex]3x - 5x = -2x[/tex], and [tex]2x^2 - x^2[/tex]= [tex]x^2[/tex]. So, the expression becomes:
[tex]-2x + x^2[/tex]
To simplify the expression [tex]-3(2x - 8) + 4x[/tex], we can start by using the distributive property to get:
[tex]-3(2x - 8) + 4x = -6x + 24 + 4x[/tex]
Next, we can combine the like terms −6x and 4x to get:
[tex]-6x + 4x + 24 = -2x + 24[/tex]
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Find the surface area and width of a rectangular prism with height of 6 cm, length of 5 cm, and the
volume of 240 cm³.
Answer:
236 cm^2 and 8 cm
Step-by-step explanation:
width=w
240=6(5)(w)
w=8 cm
area=2[(6)(5)+(6)(8)+(5)(8)]
area=236 cm^2