Rounding to two decimal places, the area of the sector is approximately 67.02cm².
What is area?Area is a measurement of the size of a two-dimensional surface, such as the surface of a flat object or the ground. It is expressed in units of square units, such as square meters or square feet.
Here,
To find the area of the sector of a circle, we need to know the measure of the central angle and the radius of the circle. In this case, we are given that the central angle is 120° and the radius of the circle is 8cm. We can use the formula for the area of a sector of a circle:
Area of sector = (central angle/360°) x πr²
where r is the radius of the circle and π is a constant approximately equal to 3.14.
Plugging in the values we have:
Area of sector = (120°/360°) x π(8cm)²
Area of sector = (1/3) x π(64cm²)
Area of sector = (1/3) x 201.06cm²
Area of sector = 67.02cm²
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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.
which statement about random sampling is true? responses random sampling helps to increase sample size. random sampling helps to increase sample size. random sampling helps to decrease sample size. random sampling helps to decrease sample size. random sampling helps to increase bias. random sampling helps to increase bias. random sampling helps to reduce bias.
The statement "random sampling helps to reduce bias" is true. Random sampling is a statistical technique where each member of the population has an equal chance of being included in the sample.
How this statement is true?By randomly selecting participants, the sample is more likely to be representative of the population, which helps to reduce bias.
Random sampling helps to reduce bias because it eliminates systematic bias, which can occur when certain individuals or groups are overrepresented or underrepresented in the sample.
For example, if a researcher only sampled individuals from a certain demographic group, the results of the study may not be generalizable to the larger population.
Random sampling also helps to increase the precision of the estimate of the population parameter, as it reduces the variability in the sample. This allows researchers to draw more accurate conclusions about the population based on the sample data.
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mrs. blue wants her students to be able to write two column geometric proofs. which is the most appropriate way to determine their mastery?
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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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
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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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]
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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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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How does the volume of a triangular prism change if it’s height is cut in half
The volume of a triangular prism will be reduced to half of it if the height is reduced by half
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces. The volume of a prism is generally expressed as ;
V = base area × height
If the height is cut into half, then the volume will be affected in this way.
V = bh, where b is the base area and h is the height.
When the height is cut into half i.e h/2 then the volume will be;
V = b × h/2
Since the base is constant, this means the volume will also be reduced by half.
Therefore when the height is reduced to half the volume is also reduced to half.
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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
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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the axis of symmetry for a quadratic equation can be found using the formula , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. what is the equation when solved for a?
The value of a is a = -b/2x
What Is Quadratic Equation?Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Suppose we have a quadratic equation of the form:
ax²+bx+c
The axis of symmetry of the parabola is :
x = -b/ 2a
From here, we must clear the value of a.
1) Pass 2a multiplying to the other side of the equation:
2ax=-b
2) Clear the value of a by passing 2x to divide:
a = -b/2x
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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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I NEED HELP ON THIS ASAP!
Answer:
I believe the answer would be 4 to the power of x?
Step-by-step explanation:
Sorry if I'm wrong but if the person is sending the selfie to four people and those four people and sending others four more pictures to other people then then you will continuously multiply 4.
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)
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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1. A rectangular fountain has an area
of (16x² + 8x + 1) ft2. The dimensions
of the rectangle have the form ax + b,
where a and b are whole numbers. Write
an expression for the perimeter of the
fountain. Then find the perimeter when
x = 2 feet.
The calculated perimeter of the fountain when x = 2 feet is 36 feet.
The area of the rectangular fountain is given by:
16x² + 8x + 1 = (4x + 1)(4x + 1)
Since the dimensions of the rectangle have the form ax + b, we can write:
Length = 4x + 1
Width = 4x + 1
The perimeter of a rectangle is given by the formula:
P = 2(L + W)
Substituting the values of L and W, we get:
P = 2(4x + 1 + 4x + 1) = 2(8x + 2) = 16x + 4
When x = 2 feet, the perimeter of the fountain is:
P = 16x + 4 = 16(2) + 4 = 32 + 4 = 36 feet
Therefore, the perimeter of the fountain when x = 2 feet is 36 feet.
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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
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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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? --
5.
Records of randomly selected births were obtained and
categorized according to the day of the week that they occurred.
A reasonable claim is that births occur on the different days with
equal frequency. Use a 0.01 significance level to test that claim.
Find the test statistic and critical value for the goodness-of-fit
needed to test the claim.
Day
Number
of Births
Sun
77
Mon
110
Tues Wed
124
122
test statistic x² = 21.005, critical value x² = 12.592
test statistic x² = 21.005, critical value x² = 16.812
Thurs
120
Fri
123
Sat
97
The critical value from the chi-square distribution table is 15.51 for 11 degrees of freedom and a 0.01 significance level. Since the chi-square statistic (23.9) is greater than the critical value (15.51), we can reject the null hypothesis
What is chi-square goodness-of-fit test?Chi-square goodness-of-fit test is used to compare observed data with theoretical data, in order to determine how closely the two sets of results match. It is used to assess whether a sample data fits a given distribution.
To test the claim that the rate of violent crime is the same for each month, we can use a chi-square goodness-of-fit test.
The null hypothesis is that the rate of violent crime is the same for each month, while the alternative hypothesis is that the rate of violent crime is not the same for each month.
The chi-square statistic is calculated as follows:
X₂ = Σ(Oi - Ei)2 / Ei
where Oi is the observed number of crimes for each month and Ei is the expected number of crimes for each month.
The expected number of crimes for each month can be calculated by dividing the total number of crimes (8,814) by 12, which gives us an expected value of 734.5.
Using these values, we can calculate the chi-square statistic:
X₂ = (786 - 734.5)2 / 734.5 + (704 - 734.5)2 / 734.5 + (835 - 734.5)2 / 734.5 + (826 - 734.5)2 / 734.5 + (900 - 734.5)2 / 734.5 + (868 - 734.5)2 / 734.5 + (920 - 734.5)2 / 734.5 + (901 - 734.5)2 / 734.5 + (856 - 734.5)2 / 734.5 + (862 - 734.5)2 / 734.5 + (783 - 734.5)2 / 734.5 + (797 - 734.5)2 / 734.5
X₂ = 23.9
We can compare this value to the critical value from the chi-square distribution table, which is 15.51 for 11 degrees of freedom and a 0.01 significance level.
Since the chi-square statistic (23.9) is greater than the critical value (15.51), we can reject the null hypothesis and conclude that the rate of violent crime is not the same for each month.
This indicates that there is a statistically significant difference in the rate of violent crime for each month.
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Find the slope between the two points (-2,3) (4,1). Then identify the line that has perpendicular slope
The slope between the two points (-2,3) (4,1) is the line perpendicular to the line through (-2,3) and (4,1) is y = 3x + 9.
To discover the slant between the two focuses (-2,3) and (4,1), able to utilize the incline equation: incline = (y2 - y1) / (x2 - x1)
slant = (1 - 3) / (4 - (-2))
= -2 / 6
= -1/3, So the slant between the two focuses is -1/3.
To discover the line that features an opposite slant, we have to keep in mind that the slants of opposite lines are negative reciprocals of each other. That's, in case the incline of one line is m, at that point the slant of a line opposite to it is -1/m.
So, the incline of the line opposite to the line through (-2,3) and (4,1) is:
-1/(-1/3) = 3
y - 3 = 3(x - (-2))
y - 3 = 3x + 6
y = 3x + 9
thus, the line perpendicular to the line through (-2,3) and (4,1) is y = 3x + 9.
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A net of a rectangular pyramid is shown.
A net of a rectangular pyramid with a base with dimensions of 13 inches by 17 inches. The two larger triangular faces have a height of 11 inches. The smaller triangular face has a height of 12.3 inches.
What is the surface area of the pyramid?
567.9 in2
457.4 in2
346.9 in2
283.95 in2
The surface area of the rectangular pyramid is approximately 567.9 in².
What is rectangular pyramid?
A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.
To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.
First, let's find the area of the rectangular base:
Area of base = length x width = 13 in x 17 in = 221 in²
Next, let's find the area of the larger triangular faces:
Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²
Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²
Finally, let's find the area of the smaller triangular face:
Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²
Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:
Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face
Total surface area = 221 in² + 187 in² + 79.95 in²
Total surface area = 488.95 in²
Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².
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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
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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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:
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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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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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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