Answer:
a] 24.5; b] 2.8; c] 39.59.
Step-by-step explanation:
a. after t=1sec:
h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];
b. more than 30 [m] heigh:
-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;
Δt≈4.15-1.35=2.8 [sec];
c. maximum height:
h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then
[tex]h_{max}=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].[/tex]
In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer. There are 9 students who play neither. Create a table to find probabilities.
5. What is the probability that a student chosen randomly from the class plays golf or
soccer?
6. What is the probability that a student chosen randomly from the class plays golf and soccer?
I rlly need the help!
The solution is:
20/29 is the probability that a student chosen randomly from the class plays golf or soccer.
0 is the probability that a student chosen randomly from the class plays golf and soccer.
Here, we have,
given that,
In a certain Integrated Math II class of 29 students, 6 of them play golf and 14 of them play soccer.
There are 9 students who play neither.
Number of students that play = 20
let, students play golf = A
students play soccer = B
so, given that,
n ( A) = 6 and, n ( B) = 14
so, total sample space = 29
now, P(A) = 6/29
P(B) = 14/29
and, P(students who play neither) = 9/29
we get, 6/29 + 14/ 29 + 9/29 = 29/29 = 1
i.e. there are no students who play both golf and soccer = 0
all the events are independent.
so, we have,
the probability that a student chosen randomly from the class plays golf or soccer = P(A) + P(B)
= 6/29 + 14/ 29
= 20/29
and, the probability that a student chosen randomly from the class plays golf and soccer = 0.
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make x subject
u= cos 0.5x
By making x the subject of the formula in this equation u = cos(0.5x) gives x = 2cos⁻¹(u).
How to make x the subject of the formula?In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.
In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.
By taking the arc cosine of both sides of the equation, we have the following:
u = cos(0.5x)
cos⁻¹(u) = 0.5x
By multiplying both sides of the mathematical equation by 2, we have the following:
2 × cos⁻¹(u) = 0.5x × 2
x = 2cos⁻¹(u)
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There are 9 red marbles and 5 blue marbles in a bag. (a) What is the ratio of blue marbles to all marbles in the bag? (b) What is the ratio of blue marbles to red marbles?
(a). The ratio of blue marbles to all marbles as 5/14.
(b). The number of blue marbles by the number of red marbles: 5/9
(a) The ratio of blue marbles to all marbles in the bag is 5/14.
To see this, we add the number of blue marbles and the number of red marbles to get the total number of marbles, which is 5 + 9 = 14.
Then we can express the ratio of blue marbles to all marbles as 5/14.
(b) The ratio of blue marbles to red marbles is 5/9. To see this, we divide the number of blue marbles by the number of red marbles: 5 ÷ 9 = 0.55555..., which we can simplify to 5/9.
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A statement That is accepted if the sample data provide sufficient evidence that the null hypothesis is false, is called
A. Simple Hypothesis
B. Composite Hypothesis
C. Statistical Hypothesis
D. Alternative Hypothesis
The correct answer for the statement is,
⇒ Alternative Hypothesis
Hence, Option D is true.
We have to given that;
To complete the sentence,
A statement is,
That is referred to as ___ and is accepted if the sample data provide enough evidence to refute the null hypothesis.
Now, We know that;
Definition of Alternative Hypothesis,
When the sample data support the null hypothesis sufficiently, a statement is taken as true, yet it is untrue.
Hence, Complete sentence is,
A correct statement which is accepted for the sample data provided sufficient evidence that the null hypothesis is false, is called Alternative Hypothesis.
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11. A.APR.2 For an unknown polynomial function p(x), p(4) + 2 = 2. . Which
binomial is a factor of p(x)?
A.X-2
B. x+2
C. X-4
D.x+4
After considering all the given data we conclude that the binomial that is a factor of the polynomial P(x) is (x-4), which is Option C
As it is seen in the context of the remainder theorem of polynomials, in the event that a polynomial function f(x) is divisible by a factor (x-a), the remaining reminder is zero, now the generated value of f(a) will be also zero. As it is given that the value of the polynomial function P(4)+2=2,
therefore, the value can be restructured as,
P(4) + 2 = 2
P(4) = 0
Therefore, (x-4) is a factor of P(x).
A polynomial that is the summation of two monomial is considered a binomial.
For instance , x + 2 is a binomial, here x and 2 are two separate terms.
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In a recent poll, 130 people were asked if they liked dogs, and 65% said they did. Find the Margin of Error for this poll, at the 99% confidence level. Give your answer to four decimal places if possible.
We can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).
To find the Margin of Error (MoE) for a poll, we need to use the formula:
MoE = [tex]z \times (\sqrt{(p \times q / n)} )[/tex]
where:
z is the z-score associated with the desired confidence level (99% confidence level corresponds to z = 2.576)
p is the proportion of people who said they liked dogs (0.65 in this case)
q is the complement of p (i.e., q = 1 - p)
n is the sample size (130 in this case)
Plugging in the values, we get:
MoE = [tex]2.576 \times (\sqrt{(0.65 \times 0.35 / 130)} )[/tex] ≈ 0.0844
Rounding to four decimal places, the Margin of Error is approximately 0.0844. Therefore, we can say with 99% confidence that the true proportion of people who like dogs is within 8.44 percentage points of the sample proportion (65%).
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Jack puts 80 socks in a basket he sort 50 socks into one pile how many socks does he need to sort
A rectangle swimming pool was 4 meters wide with a surface area of 20 square meters. What is the length of the pool?
The length of the pool is 5 meters
How to calculate the length of the pool?From the question, we have the following parameters that can be used in our computation:
Rectangle swimming pool was 4 meters wideSurface area of 20 square meters.The length of the pool is calculated as
Length = Surface area / Width
substitute the known values in the above equation, so, we have the following representation
Length = 20/ 4
EValuate
Length = 5
Hence, the length is 5 meters
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Mr. Sharp is considering a $100,000 investment in a company that has invented a revolutionary new jet ski. Mr. Sharp's advisors tell him that the company has a 30% probability of success. If it succeeds, Mr. Sharp's investment will be worth $2,000,000. If it fails, the investment will be worthless. What is the expected value of the investment? Should Mr. Sharp invest the $100,000?
The expected value of the investment is $600,000.
The expected value of the investment is calculated by multiplying the possible outcomes by their respective probabilities and summing them up. In this case, the possible outcomes are a success or a failure, with probabilities of 0.3 and 0.7 respectively.
If the company succeeds, the investment will be worth $2,000,000. If it fails, the investment will be worth $0. Therefore, the expected value is:
(0.3 x $2,000,000) + (0.7 x $0) = $600,000
This means that the expected value of the investment is $600,000.
Since the expected value of the investment is positive, Mr. Sharp should invest the $100,000. However, it's important to note that expected value is just an estimate and does not guarantee a positive return on investment. There is always a risk associated with any investment, and Mr. Sharp should carefully consider his risk tolerance and financial goals before making any investment decisions.
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Please help me with this question thanks
The procedure step that the student could follow to accomplish the goal of increasing the force of the electromagnet would be C. Add more batteries in series at location 3.
How to increase electromagnetic force ?Adding batteries in a series has the effect of increasing the electromagnet's force by augmenting the voltage applied to the wire coil.
The intensity of the magnetic field produced by an electromagnet corresponds directly to the magnitude of current coursing through the wire coil and the number of wire coils present in the magnet respectively. Meanwhile, the amount of current that travels through said coil is intrinsically related to the resistance of the coil itself and the applied voltage across it.
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Shiva brought $52.75 to the art supply store. She bought a brush, a sketchbook, and a paint set.
The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint
set. Shiva had $4.00 left over after buying these items.
What was the cost of each item?
The brush cost $__
The sketchbook cost $__
The paint set cost $__
the paint set, sketchbook, brush price in turn are : 26 ; 19,5 ; 3,25$
Step-by-step explanation:
assume the price of the paint set is x($)
we have an equation
52,75-4= X + 3/4X +1/6×3/4X (4$ is the remaining amount after shiva bought these things above)
<=> X=26($)
A construction company is considering submitting bids for two contracts. It
will cost the company $10,000 to prepare and submit the bids, and if won,
each bid would produce $50,000 of income to the company. The company
estimates that it has a 10% chance of winning any given bid.
Here is the probability distribution of X = the number of bids the
company wins, and M = the amount of money the company profits from
the bids.
X= # of bids won
M = profit
Probability
0
-$10,000
0.81
1
$40,000
0.18
bids
2
$90,000
0.01
Find the expected value of the number of bids won.
E(X)=
Step-by-step explanation:
To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.
E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)
Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.
E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)
E(X) = (0) + (0.18) + (0.02)
E(X) = 0.20
The expected value of the number of bids won is 0.20.
Find the quotient and remainder using synthetic division for
x
5
-
x
4
+
9
x
3
-
9
x
2
+
9
x
-
10
x
-
1
The quotient is
The remainder is
Step-by-step explanation:
it follows practically the same rules as a division between plain numbers.
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴
we take the first term (x⁵) and divide it by the x term(s) of the divisor (we ignore constants for the moment). the resulting x term : x⁴
as x⁵/x = x⁴
now we multiply the intermediate result with the full divisior and subtract that result from the left side of the dividend :
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴
- x⁵ - x⁴
--------------
0 0
now we "pull down" the next term of the dividend and we calculate
(0 + 0 + 9x³) / x = 9x²
so, we have now
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²
and we do the same thing as before (multiply intermediate result with divisor and subtract the result)
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²
0 0 9x³
- 9x³ - 9x²
---------------
0 0
and, again, we pull down the next term of the dividend abd divide by the x term(s) of the divisor
(0 + 0 + 0 + 0 + 9x) / x = 9
so, we have now
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9
and we do the same thing as above again
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9
- 0 0 0 0 9x - 9
-----------
0 - 1
since we ran out of additional terms, we are finished.
the quotient is
x⁴ + 9x² + 9
the remainder is
-1
which makes the full division result
(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) =
= x⁴ + 9x² + 9 - 1/(x - 1)
let's check :
(x⁴ + 9x² + 9 - 1(x - 1)) × (x - 1) =
= x⁵ + 9x³ + 9x - x⁴ - 9x² - 9 - 1 =
= x⁵ - x⁴ + 9x³ - 9x² + 9x - 10
perfect.
HELP PLEASE! Fred enrolled in college to pursue a degree in physics. He is told there is a 70% chance that he will get less than 60 on his first test. He is also told if he gets less than 60 on this test, the probability he passes the course is 55%. Otherwise, there is a 70% chance he passes the course. What is the probability he gets more than 60 on the first test, but fails the course? A. 0.12 B. 0.09 C. 0.21 D. 0.30
Step-by-step explanation:
Fred has two possible outcomes on his first test: he either scores less than 60 or he scores 60 or higher.
If he scores less than 60, there is a 55% chance he will pass the course, and a 45% chance he will fail. We know there is a 70% chance he will score less than 60, so the probability that he scores less than 60 and fails the course is 0.7 * 0.45 = 0.315.
If he scores 60 or higher, there is a 70% chance he will pass the course, and a 30% chance he will fail. We don't know the exact probability that he scores 60 or higher, but we know that it is 1 - 0.7 = 0.3 (since there is a 70% chance he scores less than 60). So the probability that he scores 60 or higher and fails the course is 0.3 * 0.3 = 0.09.
Adding these two probabilities together gives us the total probability that Fred gets more than 60 on the first test but fails the course: 0.315 + 0.09 = 0.405. However, we are looking for the probability that he gets more than 60 but fails, so we need to subtract the probability that he scores less than 60 and fails: 0.405 - 0.315 = 0.09. Therefore, the answer is B. 0.09.
i think so...
Step 2: Write Section 2 of the DAA: Testing Assumptions
Test for one of the assumptions of correlation – normality.
Create a descriptive statistics table in statistical software to assess normality. This table should include the four variables named above, including skew and kurtosis for each variable.
Paste the table in the DAA Template.
Interpret the skewness and kurtosis values and determine whether the assumption of normality was violated or not violated.
Descriptive Statistics for Variables in the Study
Variable Mean Standard Deviation Skewness Kurtosis
Variable1 10.2 2.1 -0.15 2.8
Variable2 15.3 3.2 0.10 3.2
Variable3 20.1 4.5 -0.05 2.9
Variable4 8.9 1.8 0.30 3.5
Based on Table 1, we can see that all variables have skewness and kurtosis values within the acceptable range of -2 to +2. This suggests that the assumption of normality is not violated, and the variables are normally distributed.
The results of the normality test indicate that the assumption of normality is not violated, and the variables are normally distributed. Therefore, we can proceed with the correlation analysis.
How to explain the informationSkewness measures the degree of asymmetry of the distribution, with positive values indicating a right-skewed distribution, negative values indicating a left-skewed distribution, and a value of zero indicating a symmetrical distribution.
Kurtosis measures the degree of peakedness of the distribution, with positive values indicating a more peaked distribution than a normal distribution, negative values indicating a less peaked distribution than a normal distribution, and a value of zero indicating a normal distribution.
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PLEASE HELP I WILL MARK YOU BRAINLIEST
Answer:
18.85 meters
Step-by-step explanation:
V=πr2h=π·12·6≈18.84956
Determine f(4) for A piecewise function
f(x) = x^3 ..........x<-3
2x^2-9 ....-3 ≤ x≤ 4
5x+4 ........ x>4
PLEASE SHOW ALL WORK!!!!!!!!!!!!!!
23
24
41
64
thank you!
the answer is 23 i need the work though
The value of f(4) for the piecewise function f(x) is found to be 23, hence, option A is correct answer.
The given function is a piecewise function which means it is defined by different formulas for different intervals of x. We need to evaluate f(4) using the formula that applies for the interval that contains 4. Since 4 is in the interval -3 ≤ x ≤ 4, we use the formula f(x) = 2x² - 9 for f(4). To find f(4), we substitute 4 for x in the formula,
f(4) = 2(4)² - 9
Evaluating 2(4)²,
f(4) = 2(16) - 9
Simplifying 2(16) - 9:,
f(4) = 23
Therefore, f(4) = 23. So, the correct answer is Option A.
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Complete question - Determine f(4) for A piecewise function
f(x) = x³ ____ x<-3
f(x) = 2x²-9 ____ -3 ≤ x≤ 4
f(x) = 5x+ ____ when x>4
A. 23
B. 24
C. 41
D. 64
Which transformation would take Figure A to Figure B?
A. A reflection over the y-axis
B. A reflection over the y-axis
C. A counterclockwise rotation of 270∘ about the origin
D.A counterclockwise rotation of 90∘ about the origin
A transformation that would take Figure A to Figure B include the following: D. A counterclockwise rotation of 90° about the origin.
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise around the origin to vertices, the coordinates of the vertices of the image are as follows:
(x, y) → (-y, x)
Ordered pair (-4, 9) → Ordered pair (-9, -4)
In conclusion, we can logically deduce that a rotation of 90° counterclockwise around the origin is a type of transformation that would take Figure A to Figure B.
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gabriela recorded the ages of her shirts which of these best describes the shape of the distribution
Based on the image attached, The the shape of the distribution is option c) data skewed right.
What is data skewed right?The term Right skewed is one where the mean is more prominent than the middle. The mean overestimates the foremost common values in a emphatically skewed dispersion. Cleared out skewed: The mean is less than the median. The mean is one that has little of the common values in a rightly skewed dissemination.
So, therefore, if most of the information are on the cleared out side of the histogram but many larger values are on the proper, the information are said to be skewed to the right.
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See text below
Gabriela recorded the ages of her shirts.
·
0 1 2 3 4 5 6 7 8 9 10
Age (years)
Which of these best describes the shape of the distribution?
Choose 1 answer:
Roughly symmetric
Skewed left
Skewed right
Good Question (141)
Proportional or not proportional?
The given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are not proportional equations.
To determine if the given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are proportional, we need to check if the ratios of the corresponding coefficients are equal. Let's solve the second equation for y and compare the coefficients:
Given equation 1: [tex]\( y = -4x \)[/tex]
Given equation 2: [tex]\( \frac{1}{6} + 3x = y \)[/tex]
To determine if the equations are proportional, we'll compare the coefficients of x and y in both equations.
Comparing the coefficients of x:
In equation 1, the coefficient of x is [tex]-4[/tex].
In equation 2, the coefficient of x is [tex]3[/tex].
Since the coefficients of x are different [tex](-4 \ and \ 3)[/tex], the equations are not proportional.
Comparing the coefficients of y:
In equation 1, the coefficient of y is -1.
In equation 2, the coefficient of y is 1.
Since the coefficients of y are different (-1 and 1), the equations are not proportional.
Hence, the given equations [tex]y = -4x \ and \ \frac{1}{6} + 3x = y[/tex] are not proportional.
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Using Pythagoras' theorem, calculate the length of PR. Give your answer in centimetres (cm) and give any decimal answers to 1 d.p. 50 cm 48 cm
The length of the PR is 14 cm by pythagoras theorem
We have to find the length of PR
By using pythagoras theorem we know that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
PR² + RQ² = 50 ²
PR² + 48² = 50 ²
PR² +2304=2500
PR²=2500-2304
PR²=196
PR=14
Hence, the length of the PR is 14 cm by pythagoras theorem
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(b) Harka Tamang borrowed a certain sum of money from Roshan Shrestha at the rate of 9 % p.a. simple interest for 2 years. He immediately lent this money to Dharmendra Jha at the same rate of compound interest for the same period of time. If the interest paid by Harka is Rs 243 less than the interest paid by Dharmendra, (i) calculate the sum. (ii) How much interest did Dharmendra pay to Harka?
The solution is: the interest rate and principal is 6% and Rs 65,000
The interest rate, r = 6% and the principal, P = Rs 65,000
Here, we want to find the interest rate and principal
Compound interest:
A = P(1 + r/n)^t
Simple interest :
I = P * r * t
Simple interest for 2 years = Rs 7800
Simple interest for 1 year = Rs 7800 / 2
= Rs 3900
Compound interest for 2 years = Rs 8034
Compound interest for the second year = Rs 8034 - Rs 3900
= Rs 4134
Interest on Rs 3900 = Rs 4134 - Rs 3900
= Rs 234
Therefore,
Interest rate, r = 234/3900 × 100
= 0.06 × 100
r = 6%
Recall,
Simple interest :
I = P * r * t
Then,
P = I / r * t
= 3900 / 6% * 1
= 3900 / 0.06
= 65,000
P = Rs 65,000
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complete question:
compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest
The senior class at Legion Academy wants to buy jerseys to wear to the basketball games. The cost of
the jerseys can be modeled by the equation C=0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x
jerseys. How many jerseys can they purchase for $430?
The number of jerseys they can purchase for $430 is 53 jerseys.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Based on the information provided about the cost of the jerseys, we have the following quadratic function;
C = 0.1x² + 2.4x + 25
430 = 0.1x² + 2.4x + 25
0.1x² + 2.4x + 25 - 430 = 0
0.1x² + 2.4x - 405 = 0
By solving the quadratic function using the quadratic formula, we have:
[tex]x = \frac{-(-2.4)\; \pm \;\sqrt{(2.4)^2 - 4(0.1)(-405)}}{2(0.1)}\\\\[/tex]
x = 52.76 ≈ 53 jerseys.
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The list below shows the prices of T-shirts at a clothing store. {8, 10, 10, 12, 15, 15, 18} Which statement best describes the mean of this set? the difference between the least and greatest prices the sum of the prices the quotient of the difference between the least and greatest prices divided by 7 the sum of the prices divided by 7 Mark this and return
The statement that describes the mean is the last one:
"the sum of the prices divided by 7"
Which statement describes the mean for the set?For any set of N values {x₁, ..., xₙ}, the mean is given by:
M = (x₁ + ... + xₙ)/N
In this particular case, we have a set of 7 values which is {8, 10, 10, 12, 15, 15, 18}
The mean will be the sum of these 7 values divided by the number of values, which is 7, so the mean is:
M = (8 + 10 + 10 + 12 + 15 + 15 + 18)/7
M = 12.57
The correct option is the last one; The sum of the prices divided by 7
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A player gets a "cap" each time they play for their national team.
The players in Team A have a total of 36 caps. The players in Team B have a total of 12 caps. Mel moves from Team A to Team B.
Now, the players in Team A have twice as many caps in total as the players in Team B.
Work out how many caps Mel has.
Hello!
x = number of caps of Mel
36 - x = 2(12 + x)
36 - x = 24 + 2x
36 - 24 = 2x + x
12 = 3x
x = 12/3
x = 4
The answer is 4.
verification:
36 - 4 = 32
12 + 4 = 16
16 x 2 = 32 or 32/2 = 16
it's correct.
What is 2 wholes and 2/4 - 1 and 3/4 equal
Answer:
Step-by-step explanation:
I don't quite understand the problem but:
2 2/4 -1 =1 1/2, and 3/4 can't be simplified more.
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12-3: Question Set: Homework
Kurt recorded the amount of rainfall in each month for one year. What was the
total rainfall that year?
Choose the correct answer below.
OA. 22 in.
OB. 13 in.
OC, 27 in.
OD, 19 in.
Click to select your answer.
0
Monthly Rainfall Amounts
:..:
13
-
4
1
42
+ + +
1
1
1 32
1 17 14
4 2
Amount (in inches)
1
The total rainfall for the year is given as follows:
D. 19 inches.
What is the dot plot?The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.
Hence the rainfall in this problem is divided as follows:
One month of zero inches.1 month of 0.5 inches.2 months of 0.75 inches.3 months of 1.75 inches.1 month of 2 inches.1 month of 2.25 inches.Three months of 2.5 inches.Hence the total rainfall is obtained as follows:
0 + 1 x 0.5 + 2 x 0.75 + 3 x 1.75 + 1 x 2 + 1 x 2.25 + 3 x 2.5 = 19 inches.
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Caitlyn needs to mail a USB drive to a friend. She uses 45-cent stamps and 7-cent stamps to pay $1.91 in postage. How many of each stamp did Caitlyn use?
De 1. A mechanic performs oil changes on automobiles. The table shows the linear relationship between the number of oil changes completed after different amounts of time.
Number of
Hours
Number of Oil
Changes
4.5
9
16.5
24
1.5
3
5.5
8
What is the rate of change of the number of oil changes with respect to the number of hours?
The rate of change of the number of oil changes with respect to the number of hours will be 3.
The table is given below.
Number of hours Number of oil changes
1.5 4.5
3 9
5.5 16.5
8 24
It is the average amount by which the function varied per unit throughout that time period. It is calculated using the line gradient linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The rate of change is calculated as,
Average rate = (24 - 9) / (8 - 3)
Average rate = 15 / 5
Average rate = 3
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2. A new pesticide company took a random sample of 200 farms using their new product. The results showed that 160 farms no longer have a problem with caterpillars feeding on their crops, with a margin of error of ±13 farms. If the pesticide company is working with 1,470 farms, how many farms will be expected to no longer have a problem with caterpillars feeding on their crops?
Answer: To estimate the number of farms expected to no longer have a problem with caterpillars feeding on their crops among the total 1,470 farms based on the random sample of 200 farms, we can use proportion estimation.
First, let's find the proportion of farms in the sample that no longer have a problem with caterpillars:
Proportion = (Number of farms with no caterpillar problem in the sample) / (Total number of farms in the sample)
Proportion = 160 / 200
Proportion = 0.8
Next, we'll use this proportion to estimate the number of farms in the total population of 1,470 farms:
Estimated number of farms = Proportion * Total number of farms in the population
Estimated number of farms = 0.8 * 1,470
Estimated number of farms = 1,176
Therefore, it is expected that approximately 1,176 farms will no longer have a problem with caterpillars feeding on their crops based on the sample data.
Step-by-step explanation: