The sum of two numbers is 80 The difference is 16 Write and solve a system of equations to find the numbers.

Answer: 5 + 47 = 108

Step-by-step explanation: dont worry it works

Answer:

pythagoras thoerem

Step-by-step explanation:

y squared = 10 squared - 7 squared

y = 100 - 49= 51

y square root of 51 =7.1

Answer:

F(x)=h(x)-8

I think

Step-by-step explanation:

Answer:

grab objects

Step-by-step explanation:

barrels and things like that would most likely grab objects so the fish can have room to swim and stuff

The mean of the finishers in the New York City 10-km run is 60 minutes and standard deviation is 9 minutes.

To determine the percentage of finishers who have times between 55 and 75 minutes, we need to find the Z-scores for both of these values as follows:

Z1 = (55 - 60) / 9 = -0.56Z2 = (75 - 60) / 9 = 1.67

Now, we need to find the area under the standard normal distribution curve between these two Z-scores as follows:

P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56) Using a standard normal distribution table,

we can find the probabilities as:

P(Z < 1.67) = 0.9525P(Z < -0.56) = 0.2881

Therefore , P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56)= 0.9525 - 0.2881= 0.6644Therefore, the percentage of finishers who have times between 55 and 75 minutes is 66.44%.

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Answer:

5a - 3

Step-by-step explanation:

3a + 2a = 5a

1 - 4 = -3

5a + (-3) or 5a - 3

Answer:

546

Step-by-step explanation:

3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.

Answer:

72

Step-by-step explanation:

Answer:

72 units

Step-by-step explanation:

The Pythagorean Theorem states that [tex]a^2+b^2=c^2[/tex] in a right triangle when a and b are the two legs and c is the hypotenuse (the longest side).

[tex]a^2+b^2=c^2[/tex]

In the diagram, 30 measures one of the legs and 78 measures the hypotenuse. Plug these in as a and c.

[tex]30^2+b^2=78^2\\900+b^2=6084[/tex]

Subtract 900 from both sides

[tex]900+b^2-900=6084-900\\b^2=5184[/tex]

Take the square root of both sides

[tex]900+b^2-900=6084-900\\\sqrt{b^2} =\sqrt{5184}\\b=72[/tex]

Therefore, the length of the missing side is 72 units.

I hope this helps!

If you made this Very good job. I like it, and its hard to make a song i like. i like about 60 songs total out of the 10000+ ik of

Answer:

x-intercept

y-intercept

Step-by-step explanation:

Answer:

x-intercept y-intercept

Based on the results, we can observe that as x approaches 2, the slopes of PQ are getting closer to 4. Therefore, we can guess that the slope of the tangent line to the curve at P(2,12) is approximately 4.

To find the slope of the secant line PQ, we need to determine the coordinates of point Q and then calculate the slope using the formula:

slope = (change in y) / (change in x)

Given that Q is the point (x, x^2 + x + 6), we can substitute the values of x to find the corresponding slopes.

If x = 2.1:

Q = (2.1, (2.1)^2 + 2.1 + 6) = (2.1, 12.51)

Slope of PQ = (12.51 - 12) / (2.1 - 2) = 0.51 / 0.1 = 5.1

If x = 2.01:

Q = (2.01, (2.01)^2 + 2.01 + 6) = (2.01, 12.0601)

Slope of PQ = (12.0601 - 12) / (2.01 - 2) = 0.0601 / 0.01 = 6.01

If x = 1.9:

Q = (1.9, (1.9)^2 + 1.9 + 6) = (1.9, 11.61)

Slope of PQ = (11.61 - 12) / (1.9 - 2) = -0.39 / -0.1 = 3.9

If x = 1.99:

Q = (1.99, (1.99)^2 + 1.99 + 6) = (1.99, 11.9601)

Slope of PQ = (11.9601 - 12) / (1.99 - 2) = -0.0399 / -0.01 = 3.99

Based on the results, we can observe that as x approaches 2, the slopes of PQ are getting closer to 4. Therefore, we can guess that the slope of the tangent line to the curve at P(2,12) is approximately 4.

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Answer: Big rectangle shades 1/4+1/2

Step-by-step explanation:

So have a Big

Answer:

5

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Number of comedy = 6

Number of action = 4

Number of drama = 2

Selecting one of each ; total Number of possible combinations ;

nCr

Comedy = 6C1

Action = 4C1

Drama = 2C1

6C1 * 4C1 * 2C1 = 6 * 4 * 2 = 48

Answer: 9π≈28.26 squared units

Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.

Step-by-step explanation:

From the table, let's extract a set of data.

let's take x = 3, y = -9.

Let's substitute x into each of the equation to check.

A.

[tex]y = \frac{x}{ - 3} \\ y = \frac{3}{ - 3} \\ = - 1[/tex]

From here we can see the calculated y is not equal to the y in the table, therefore this cannot be the answer.

B.

[tex]y = x \\ y = - 3[/tex]

From here we also can see the calculated y is not equal to the y in the table, therefore this also cannot be the answer.

C.

[tex]y = 3x \\ = 3( - 3) \\ = - 9[/tex]

From here we can see the calculated y is equal to the y in the table , therefore this is the answer.

D.

[tex]y = - 3x \\ = - 3( - 3) \\ = 9[/tex]

From here we can see the calculated y is not equal to the y in the table, therefore this is not the answer.

Answer:

36%

Step-by-step explanation:

30/2500 x 30/2500=

900/2500=0.36

0.36*100=36%

For a real number x, by using mathematical induction it is shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx for every positive integer n.

To prove the inequality a[tex](1 + x)^{2n}[/tex] > 1 + 2nx  for every positive integer n, we will use mathematical induction.

The inequality holds true for n = 1, and we will assume it is true for some positive integer k.

We will then show that it holds for k + 1, which will complete the proof.

For n = 1, the inequality becomes a[tex](1 + x)^2[/tex] > 1 + 2x.

This can be expanded as a(1 + 2x + [tex]x^2[/tex]) > 1 + 2x, which simplifies to a + 2ax + a[tex]x^2[/tex] > 1 + 2x.

Now, let's assume the inequality holds true for some positive integer k, i.e., a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.

We need to prove that it holds for k + 1, i.e., a[tex](1 + x)^{2(k+1)}[/tex] > 1 + 2(k+1)x.

Using the assumption, we have a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.

Multiplying both sides by [tex](1 + x)^2[/tex], we get a[tex](1 + x)^{2k+2}[/tex] > (1 + 2kx)[tex](1 + x)^2[/tex].

Expanding the right side, we have a[tex](1 + x)^{2k+2}[/tex] > 1 + 2kx + 2x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].

Simplifying further, we get a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].

Since k and x are positive, 2k[tex]x^2[/tex] and 2[tex]x^2[/tex] are positive as well.

Therefore, we can write a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex] > 1 + 2(k+1)x.

This proves that if the inequality holds for some positive integer k, it also holds for k + 1.

Since it holds for n = 1, it holds for all positive integers n by mathematical induction.

Therefore, we have shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx  for every positive integer n.

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The profit function if the cost and revenue is given  P(x) = -0.01x² + 3.2x - 150.

To find the profit function P(x), we subtract the cost function C(x) from the revenue function R(x). This gives us the expression for P(x) as P(x) = R(x) - C(x).

The profit function P(x) represents the difference between the revenue R(x) and the cost C(x). To find P(x), we subtract C(x) from R(x):

P(x) = R(x) - C(x)

Substituting the given expressions for R(x) and C(x), we have:

P(x) = (9x - 0.01x²) - (150 + 5.8x)

Simplifying this expression, we get:

P(x) = 9x - 0.01x² - 150 - 5.8x

Combining like terms, we have:

P(x) = -0.01x² + 3.2x - 150

Thus, the profit function is given by P(x) = -0.01x² + 3.2x - 150. This function represents the profit made as a function of the quantity of goods sold, x. It allows us to analyze the relationship between revenue, cost, and profit for different values of x.

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Answer:

28.27 rounded orrrr 28.27433388 not rounded.

Step-by-step explanation:

area of circle=πr^2

radius=3 km

3^2=9

9*π

Step-by-step explanation:

Area of a circle = πr²

Radius (r) =1/2 Diameter

=60/2

=30km

Area = π x (30)²

= π x 900

= 2027km²

Answer: 98

Step-by-step explanation: According to the corresponding angles theorem m<1=82. Then according to the linear supplements theorem m<2=98. Hope this helps!

Answer:

98°

Step-by-step explanation:

Angle 1 also measures 82° because it is a corresponding angle to the given angle. Angles 1 and 2 are supplementary and therefore must add up to 180°.

Answer:

50°

Step-by-step explanation:

We are to find m ∠2

And lines A and B are parallel

m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°

Hence,

m ∠2 = 50°

Therefore, m ∠2 = 50°

Answer:

1,512

Step-by-step explanation:

36x42

Answer: just simplify condense it then your answer will be log(16)

Answer:

7m and 49 m^2

Step-by-step explanation:

i am not sure on the second answer

Answer:

(x1, y1) = (1, 3)

(x2, y2) = (4, 12)

Step-by-step explanation:

y= x^2 - 4

y= 5x - 8

(substitute the value for y)

x^2 - 4 = 5x - 8

(solve the equation)

x = 1

x = 4

(substitute the values)

y = 5 × 1 - 8

y = 5 × 4 - 8

(solve the equations)

y = -3

y = 12

( the possible solutions are)

x1, y1 = 1, -3

x2, y2 = 4, 12

(check the solutions)

-3 = 1^2 - 4

-3 = 5 × 1 - 8

12 = 4^2 - 4

12 = 5 × 4 - 8

(simplify)

-3 = -3

-3 = -3

12 = 12

12 = 12

(the ordered pairs are the solutions)

a) The Z-value corresponding to a confidence level of 95% can be determined as 1.96.

b) To determine the required sample size, we need additional information such as the population size or an estimated proportion. Without this information, we cannot calculate the sample size.

a) The Z-value represents the number of standard deviations a data point is from the mean in a standard normal distribution. For a confidence level of 95%, which corresponds to a 5% significance level, the critical Z-value is approximately 1.96. This value can be obtained from a Z-table or using statistical software.

b) To calculate the required sample size, additional information is needed, such as the population size or an estimated proportion. The sample size formula takes into account factors such as the desired margin of error, confidence level, and variability. Without these details, it is not possible to determine the sample size accurately.

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Answer:

5.06 years or 60.75 months

Step-by-step explanation:

Compound interest formula:

[tex]AV=PV(1+\frac{i}{n})^{n*t}\\4045=3355(1+\frac{.037}{12})^{12t}\\1.025=(1.003)^{12t}\\log1.025_{1.003}=12t\\60.75=12t\\5.062[/tex]

5.06 years or 60.75 months

It will take Andrew  5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest to solve this problem:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

where:

A is the amount of money at the end of the investment period

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time (in years) of the investment period

In this case, we want to solve for t. We know that:

P = $3355

r = 0.037 (3.7% as a decimal)

n = 12 (compounded monthly)

A = $4045

Substituting these values into the formula, we get:

[tex]4045 = $3355(1 + 0.037/12)^(^1^2^t^)[/tex]

ln(1.206) = 12t ln(1 + 0.037/12)

ln(1.206) = 12t ln(1 + 0.0031)

ln(1.206) = 12t ln(1.0031)

0.187=12t 0.0031

0.187=0.0372t

t=5.02

Therefore, it will take Andrew approximately 5 years to accumulate $4045 by investing $3355 in an account that earns 3.7% annually, compounded monthly.

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Answer:

[see below]

Step-by-step explanation:

[tex]5(2)=7\\\\10\neq 7[/tex]

No, (2, 7) is not the answer to the equation 5x = y.

[tex]5x=y\\\\5(2)=y\\\\\boxed{10=y}[/tex]

The value of y should be 10.

Hope this helps.

Answer:

45 degree

Step-by-step explanation:

a. The null hypothesis (H0) would state that the mean recall of ad information for children who receive an audiovisual presentation is equal to the mean recall.

a.The alternative hypothesis (Ha) would state that the mean recall of ad information differs between the two groups.

b. To find the test statistic, we can use the two-sample t-test formula:

t = (x1_bar - x2_bar) / sqrt((s1^2/n1) + (s2^2/n2))

Substituting the given values:

t = (3.70 - 3.30) / sqrt((1.98^2/20) + (2.13^2/20))

c. The rejection region for a significance level of α = 0.10 in a two-tailed test can be determined using a t-table or a t-distribution calculator. Since the alternative hypothesis is two-tailed, we need to split α equally between the two tails. In this case, the rejection region would be t < -1.734 or t > 1.734.

d. Based on the test statistic value calculated in part (b), we can compare it to the rejection region. If the test statistic falls within the rejection region, we reject the null hypothesis. If it falls outside the rejection region, we fail to reject the null hypothesis. In this case, we would fail to reject the null hypothesis since the test statistic does not fall within the rejection region. Therefore, we cannot conclude that the mean recall of ad information differs between the two groups, supporting the researchers' theory.

e. The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the researchers reported a p-value of 0.62. Since this p-value is greater than the significance level of α = 0.10, it indicates that the observed data is likely to occur by chance alone assuming the null hypothesis is true. Therefore, we fail to reject the null hypothesis and cannot conclude that there is a significant difference in the mean recall of ad information between the two groups.

f. For the inference to be valid, certain conditions must be met. These conditions include random sampling, independence between observations, approximately normal distributions of the populations or large sample sizes, and equal variances between the groups. Without information about the sampling method and data characteristics, we cannot determine if these conditions were met. It is important to note that if the conditions for inference are not met, the validity and reliability of the test results may be compromised.

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