The ratio of boys to girls in Ella's grade is 3/4 the ratio of boys to girls in minhs grade is 4 to 5 each grade has a total of 20 girls how many boys are in each grade

Answer:

The probability that the answer is an even number is 50%.

Step-by-step explanation:

There are 8 terms: 8, 9, 10, 11, 12, 13, 14, 15. Even numbers: 8, 10, 12, 14. So, 4 out of the 8 terms are even, which is equivalent to 50%.

The probability that the number is an even number is 1/2.

The probability is defined as the ratio of number of favourable outcomes and the the total number of possible outcome.

A number from 8 to 15 is drawn at random.

The number between 8 to 15 are 8, 9, 10, 11, 12, 13, 14, 15 = 8

Total even number = 8, 10, 12, 14 = 4

The probability that the number is an even number is;

[tex]\rm Probability =\dfrac{Total \ even \ number}{Total \ number}\\\\Probability =\dfrac{4}{8}\\\\Probability =\dfrac{1}{2}[/tex]

Hence, the probability that the number is an even number is 1/2.

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Answer:

90 square cm.

Step-by-step explanation:

For similar figures, the length of corresponding sides are proportional.

So we can write 4k = 6 where k is the proportionality constant.

Note: In terms of area, the scale factor would be k^2 and in terms of volume, it would be k^3y

Solving 4k = 6, we see that k = 6/4 or 3/2

We need area, so we multiply area of ABC by k^2 to get area of PQR.

[tex]40(\frac{3}{2})^2\\=40(\frac{9}{4})\\=90[/tex]

Area of PQR = 90 cm^2

Answer:

The area of △PQR is [tex]90\ cm^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

so

Let

z-----> the scale factor

x---> the corresponding side triangle PQR

y---> the corresponding side triangle ABC

[tex]z=\frac{x}{y}[/tex]

substitute the values

[tex]z=\frac{6}{4}=1.5[/tex]

step 2

Find the area of triangle PQR

we know that

If two figures are similar, then the ratio of its areas  is equal to the scale factor squared

so

Let

z-----> the scale factor

x---> the area of triangle PQR

y---> the area of triangle ABC

[tex]z^{2} =\frac{x}{y}[/tex]

we have

[tex]z=1.5[/tex]

[tex]y=40\ cm^{2}[/tex]

substitute the values

[tex]1.5^{2} =\frac{x}{40}[/tex]

[tex]x=40(1.5^{2})=90\ cm^{2}[/tex]

c. 25 because she gets $25 per hour

Answer:

$255.50

Step-by-step explanation:

✯Hello✯

↪  Alright so the item is originally 365 dollars

↪  you have to work out 30% of this which is 109.50

↪  then do 365- 109.50

↪  thats $255.50

❤Gianna❤

Answer:

63%

Step-by-step explanation:

This is a problem of conditional probability.

The two events that are given are:

We have to find the probability of being stuck in the snow AND requiring a tow truck which can be given as P(S and T)

We are also given the conditional probability, which is P(T | S) = 90% = 0.90

Using the given formula for our case we can modify the formula as:

[tex]P(T|S)=\frac{P(S \cap T)}{P(S)}[/tex]

[tex]0.90=\frac{P(S \cap T)}{0.70}\\\\ P(S \cap T)=0.90 \times 0.70\\\\ P(S \cap T)=0.63[/tex]

Therefore, there is 63% (0.63) chance that you will get stuck in the snow with your car AND require a tow truck to pull you out

The probability of getting stuck in the snow and requiring a tow truck is found by multiplying the individual probabilities, resulting in a 63% chance.

The question asks for the probability that you will get stuck in the snow with your car AND require a tow truck to pull you out. To calculate this combined probability (P(A AND B)), we use the rule of multiplication for dependent events, which states P(A AND B) =[tex]P(B|A) imes P(A).[/tex] Here, P(A) is the probability of getting stuck in the snow, and P(B|A) is the probability of requiring a tow truck given that you are stuck.

In numbers, this becomes P(A AND B) = [tex]0.90 imes 0.70 = 0.63 or 63%[/tex]. Therefore, the chance that you will get stuck in the snow and require a tow truck to pull you out is 63%.

Answer:

that is a true statment.

20 - 3n = -3n + 20

Step-by-step explanation:

add the numbers, collect the like terms.

Victoria's daughter's cookies will have more butter. Victoria uses 0.68g of butter per gram of flour, whereas her daughter uses 0.85g of butter per gram of flour.

Answer:

Daughter is using 0.17 gram more butter for each gram flour.

Step-by-step explanation:

Victoria's favorite cookie recipe uses 170 grams of butter for every 250 grams of flour  = [tex]\frac{170}{250}[/tex]  = 0.68

Therefore, this recipe needs 0.68 grams of butter for every gram flour.

Her daughter made cookies using 340 grams of butter for every 400 grams of flour = [tex]\frac{340}{400}[/tex] = 0.85

She is using 0.85 grams of butter for every gram flour.

Victoria's daughter is using 0.17 gram of butter more on every gram flour.

To answer the question, a statistical hypothesis test comparing the proportions of successful repair attempts is needed. This involves calculating a Z-score and referencing Z-tables or statistical software for the p-value. Also, a one-sided 95% confidence interval needs to be calculated for the proportion differences using the Z-test.

To answer this question, we need to perform a statistical hypothesis test which involves the comparison of proportions. Let's denote p1 as the proportion of successful repairs for tears greater than 25 mm (15 successful out of 19 trials), and let p2 for tears shorter (21 successful out of 29 trials).

To find the p-value, we need to implement a Z-test using the formula Z = (p1 - p2) - 0 / sqr((p(1-p)(1/n1 + 1/n2)) where p = (x1 + x2) / (n1 + n2). By substituting the values in the formula we get our z-score, which is used to find the p-value from the Z-tables or by using statistical software.

As for the 95% confidence interval, we will also use the Z-test formula, but this time the Z-value for the 95% one-sided confidence level which is approximately 1.645. Substituting the values in we can calculate our confidence bound. Please remember that to make accurate calculations you need to use calculated Z-score and confidence interval in the Z distribution method.

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(a) The p-value is 0.1814, and we do not have evidence that the success rate is significantly greater for longer tears.

(b) The one-sided 95% confidence bound on the difference in proportions is 0.184.

To answer your question regarding the success rates of arthroscopic meniscal repair for varying tear lengths, let's break it down into two parts: (a) the p-value and the evidence regarding the success rates, and (b) calculating a one-sided 95% confidence bound on the difference in proportions.

Part (a): Evidence and p-value Calculation:-

Define Success Rates:

For tears greater than 25 mm:

For shorter tears:

Hypotheses:

Calculate the z-statistic:
The formula for the z-statistic comparing two proportions is:

[tex]z = \frac{p_1 - p_2}{\sqrt{p(1 - p)(\frac{1}{n_1} + \frac{1}{n_2})}}[/tex]
where [tex]p = \frac{x_1 + x_2}{n_1 + n_2}[/tex] is the combined proportion.

Combined proportion (p):
[tex]p = \frac{15 + 21}{19 + 29} = \frac{36}{48} = 0.75[/tex]

Z-statistic calculation:
[tex]z = \frac{0.7895 - 0.7241}{\sqrt{0.75 \times (1 - 0.75) \times \left(\frac{1}{19} + \frac{1}{29}\right)}}[/tex]

Upon performing the necessary computations:

Find the p-value:
This represents the probability of observing a value as extreme (or more extreme) than the z-statistic under the null hypothesis. Using z-tables or a calculator for a right-tailed test:

Decision:

Part (b): One-sided 95% Confidence Bound:-

Confidence Interval for the Difference in Proportions:
The formula for the confidence interval is given by:
[tex](p_1 - p_2) \pm z_{\alpha} \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]

Differences in proportions:
[tex]p_1 - p_2 = 0.7895 - 0.7241 = 0.0654[/tex]

Calculate the margin of error:
[tex]ME = z_{\alpha} \times \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]

Confidence Bound:

Result:

Answer:

the answer is 11 dollars

Step-by-step explanation:

Answer:

11 dollars

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The range is the set of ALLOWED y-values of the function (graph). Also, the range is the y-values for which the function is defined.

Looking at the graph, we see that the graph is defined between y = 1 and y = 7. So the range is  1 ≤ y ≤ 7

the correct answer is C

[tex]f(x)=3x^2-4x+1[/tex] is a polynomial and thus continuous everywhere and differentiable on any open interval. (second option)

The MVT then guarantees the existence of [tex]c\in(0,2)[/tex] such that

[tex]f'(c)=\dfrac{f(2)-f(0)}{2-0}=\dfrac{5-1}2=2[/tex]

We have

[tex]f'(x)=6x-4[/tex]

so

[tex]6c-4=2\implies6c=6\implies c=1[/tex]

The true statement is: (b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable

Mean value theorem states that:

If [tex]\mathbf{f(x)\ is\ continuous}[/tex] [a,b] and

[tex]\mathbf{f(x)\ is\ differentiable}[/tex] on (a,b),

Then there is a point c in (a,b), such that: [tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

The function is given as:

[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]

And the interval is: [tex]\mathbf{[0,2]}[/tex]

We have

[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

This becomes

[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2 - 0}}[/tex]

[tex]\mathbf{f'(c) = \frac{f(2) - f(0)}{2}}[/tex]

Calculate f(2) and f(0)

[tex]\mathbf{f(2) = 3\times 2^2 - 4\times 2 + 1 = 5}[/tex]

[tex]\mathbf{f(0) = 3\times 0^2 - 4\times 0 + 1 = 1}[/tex]

So, we have:

[tex]\mathbf{f'(c) = \frac{5-1}{2}}[/tex]

[tex]\mathbf{f'(c) = \frac{4}{2}}[/tex]

[tex]\mathbf{f'(c) = 2}[/tex]

Recall that:

[tex]\mathbf{f(x) = 3x^2 - 4x + 1}[/tex]

Differentiate

[tex]\mathbf{f'(x)= 6x - 4}[/tex]

Substitute c for x

[tex]\mathbf{f'(c)= 6c - 4}[/tex]

Substitute 2 for f'(c)

[tex]\mathbf{ 6c - 4 = 2}[/tex]

Collect like terms

[tex]\mathbf{ 6c = 4 + 2}[/tex]

[tex]\mathbf{ 6c = 6}[/tex]

Divide both sides by 6

[tex]\mathbf{c = 1}[/tex]

The interval is given as: [0,2]

The value of c is true for interval (0,2).

Hence, the true statement is:

(b) Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable

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Answer:

23

Step-by-step explanation:

3^2+(6-2)•4-6/3

Order of operations:

= 9 + (4)•4 - 6/3

= 9 + 16 - 2

= 25 -2

= 23

32+(6−2)(4)− 6/3

your answer is =23

32+(6−2)(4)− 6/3

=9+(6−2)(4)− 6/3

=9+(4)(4)− 6/3

=9+16− 6/3

=25− 6/3

=25−2

=23

Answer:

7x - 5 = 11

Step-by-step explanation:

To solve for x, substitute y = -5 into the equation 7x + y = 11.

This becomes 7x + (-5) = 11 or 7x - 5 = 11.

Answer:

101 degrees

Step-by-step explanation:

- A circle with two chords

- The two cords have common start point A on the circle

- The chord AB subtended arc AB with measure 115°

- The chord AC subtended arc AC with measure 43°

- The measure of any circle is 360°

* These two cords divide the circumference of the circle into

 three arcs, arc AB , arc AC and arc BC

∵ The measure of arc AB = 115°

∵ The measure of arc AC = 43°

∵ The measure of the circle is 360°

∴ The measure of arc BC = 360 - (115 + 43) = 360 - 158 = 202°

- In the circle, the angle whose vertex is on the circle is

called inscribed angle and subtended by the opposite arc,

its measure is half the measure of the subtended arc

∵ ∠BAC is an inscribed angle subtended by arc BC

∴ m∠BAC = 1/2 measure of arc BC

∵ The measure of arc BC = 202°

∴ m∠BAC = 202 ÷ 2 = 101°

Using the normal distribution, it is found that:

a) The percentage of men who can fit without bending is 0.02​%.

b) A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The proportion is the p-value of Z when X = 55.9, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.9 - 69.7}{3.6}[/tex]

[tex]Z = -3.83[/tex]

[tex]Z = -3.8[/tex] has a p-value of 0.0002.

0.0002 x 100% = 0.02%

The percentage of men who can fit without bending is 0.02​%.

Item b:

A very small percentage of people can fit through the door, thus the dimensions are not adequate. Possible, the engineers did not design a large door because of engineering constraints.

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Answer:

C. 7x^2 + x - 6

Step-by-step explanation:

f(x) = 2x^2 + 3x and g(x) = 5x^2 - 2x - 6

(f+g)(x) = 2x^2 + 3x + 5x^2 - 2x - 6

(f+g)(x) = 7x^2 + x - 6

Answer:

your answer is A HOPE THIS HELPS!!!

Step-by-step explanation:

Answer:

The graph B is the most appropriated

Step-by-step explanation:

Due to we need to know the charging of the company as a function of miles, it is practical to enter into the graph with the miles into the horizontal axis and obtain the charge over the vertical axis. In fact, the common usage, it is by entering the unknown quantity (independent variable) into the x-axis (horizontal axis) and looking function calculated value into the y-axis (vertical axis).  

Taking the previous into account, we chose the graph from option B.

Answer:

C. 48

Step-by-step explanation:

If you cut the circle in half through the points M and C it splits 96 in half which is 48 which is the same size as M

Answer:

Step-by-step explanation:

Look at the pictures.

(the picture 1)

Inscribed angle and central angle.

(the picture 2)

In a circle, central angle is two times larger than inscribed angle that intercept the same arc.

We have the central angle C. m∠C = 96°.

The inscribed angle M: m∠M = 96° : 2 = 48°

A Histogram would be best

To answer this we must know BIDMAS

Brackets) Let's do 8-6 as (2*3 is 6 as we substitute X with 3) and that gives us 2

Indices) Let's do 2 square which gives 4

Addition) Then finally add 4 to 4 giving us 8

The answer is 8

Answer:

The height of the tree is 18 feet tall

Step-by-step explanation:

Set up a proportion:

6 feet over 11 feet long equals x feet over 33 feet long

6/11 = x/33

198 = 11x

x = 18

The height of the tree is 18 feet tall

Answer:

the answer is 60

Step-by-step explanation:

Answer:

Step-by-step explanation:

Eliminating parentheses, you get ...

  -2bx +10 = 16

Subtract 10 and divide by -2b:

  x = 6/(-2b)

  x = -3/b

__

When b=3, you have ...

  x = -3/3

  x = -1

Answer:

B

Step-by-step explanation:

The compound interest formula is [tex]A = P (1+r/n)^nt[/tex] where:

Substitute a value into each variable to solve.

[tex]A = P (1+r/n)^{nt}\\A = 147(1 + \frac{0.035}{12})^{12*25}\\A = 147 ( 1 + 0.002916)^{300}\\A = 147(1.002916)^{300}\\A = 352.19[/tex]

Repeat this process for each formula.

Answer:

B. $352.12

B. $9,126.53

D. $123,866.02

Step-by-step explanation:

Hope this helps! Have an awesome day/night!

Answer:

Step-by-step explanation:

dimes only cannot give total ending in 5 cents

so theres at least 1 nickel

n by the same reason, no.of nickels must be odd no.

most nickels is 0.65/0.05=13

combining the above, ans is D. (1,3,5,7,9,11,13)

Answer:

The Answer Is D (1,3,5,7,9,11,13)

Step-by-step explanation:

ANSWER

[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]

EXPLANATION

If the polynomial has a root -2, with multiplicity 1, then (x+2) is a factor.

If the polynomial has root, 7 with multiplicity 1, then (x-7) is a factor.

If the polynomial has root 5, with multiplicity 2, then (x-5)² is a factor of the polynomial.

The fully factored form of the polynomial is

[tex]f(x) =a (x + 2)(x - 7) {(x - 5)}^{2} [/tex]

It was given that the polynomial has a leading coefficient of 1.

Hence a=1.

This implies that,

[tex]f(x) =(x + 2)(x - 7) {(x - 5)}^{2}[/tex]

Or

[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]

Answer:

f(x) = (x -7)(x - 5) {(x - 5)}(x + 2) the answer is D

Step-by-step explanation:

5/8=expression is equivalent to

5 8

my mom tell me this its E oksy

Answer:

Option A.

Step-by-step explanation:

It is given secθ = - [tex]\frac{4}{3}[/tex]

then cosθ = -[tex]\frac{3}{4}[/tex]

Now we know the identity

sinθ = [tex]\sqrt{1-cos^{2}\theta }[/tex]

       = [tex]\sqrt{1-(-\frac{3}{4} )^{2}}[/tex]

       = [tex]\frac{\sqrt{7} }{4}[/tex]

Now sin2θ = 2sinθcosθ

Now we put the values of cosine and sine in the formula

sin2θ = 2×(-[tex]\frac{3}{4}[/tex])([tex]\frac{\sqrt{7}}{4}[/tex])

         = -[tex]\frac{3\sqrt{7}}{8}[/tex]

Therefore, option A. is the answer.

Answer:

0.0322; 0.9929

Step-by-step explanation:

Since the data is normally distributed, we use z scores for these probabilities.

The formula for a z score of a sample mean is

[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]

For the sample of mildly obese people, the mean, μ, is 371; the standard deviation, σ, is 65; and the sample size, n, is 6.

Using 420 for X,

z = (420-371)/(65÷√6) = 49/(65÷2.4495) = 49/26.5360 ≈ 1.85

Using a z table, we see that the area under the curve to the left of this is 0.9678.  However, we want the area to the right, so we subtract from 1:

1-0.9678 = 0.0322

For the sample of lean people, the mean, μ, is 528; the standard deviation, σ, is 108; the sample size, n, is 6.

Using 420 for X, we have

z = (420-528)/(108÷√6) = -108/(108÷2.4495) = -108/44.0906 ≈ -2.45

Using a z table, we see that the area under the curve to the left of this is 0.0071.  We want the area under the curve to the right, so we subtract from 1:

1-0.0071 = 0.9929

The probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 3.2%. For the 6 lean people, this probability is approximately 0.7%.

For this type of problems, we use the concept of z-scores in statistics. The z-score is a measure of how many standard deviations a data point is from the mean. In this case, we will first calculate the standard error by dividing the standard deviation by the square root of sample size and then find the z-score by dividing the value of interest (420 minutes) minus mean by the standard error.

For mildly obese people, mean = 371 min, standard deviation = 65 min, sample size = 6. So, standard error = 65/sqrt(6) ≈26.51. The z-score for 420 min = (420-371)/ 26.51 ≈1.85. This indicates 420 minutes is 1.85 standard deviations above the mean. The probability that z-score exceeds 1.85 (assuming a one-tailed test since we are looking for the mean to be more than 420 minutes) is 0.032 (approximately). Hence, the probability that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes is about 0.032 or 3.2%.

For lean people, mean = 528 min, standard deviation = 108 min, sample size = 6. Using the same approach, standard error = 44.11. The z-score for 420 min = (420-528)/44.11 ≈-2.45. This indicates 420 minutes is 2.45 standard deviations below the mean. The probability that z-score is less than -2.45 (assuming a one-tailed test for under 420 minutes) will be more than 99%. The probability that z-score exceeds -2.45 (420 min or more time) is about 1 - 0.993 = 0.007. Hence, the probability that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes is about 0.007 or 0.7%.

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