Kali has a 6 meter ladder that she wants to use to get her cat out of a tree. She puts the base of the ladder 2 meters away from the base of the tree.

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Answer:Get a quadratic function from its roots. Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola.

Step-by-step explanation:Solve a quadratic equation using the quadratic formula.

Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c.

Write the Quadratic Formula. Then substitute in the values of a, b, and c.

Simplify.

Check the solutions.

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:

pls upload photo for your question

The answer is 2.0625

Answer:

33/16=2.0625

Step-by-step explanation:

33/16=2 rounded to the nearest integer

33/16=2.1 rounded to 1 decimal place

33/16=2.06 rounded to 2 decimal places

33/16=2.063 rounded to 3 decimal places

33/16=2.0625 rounded to 4 decimal places

Since the rectangle's shorter side is half as long as its longer side, its top left vertex is (0,a).

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y). You do the reverse to determine a point's coordinates in a coordinate system. Start at the point, then move up or down a vertical line until you reach the x-axis. Your x-coordinate is shown there. To find the y-coordinate, repeat the previous step while adhering to a horizontal line.

Here,

Let x be the length and y be the width,

y=x/2

x=2a

y=a

The top left vertex=(0,a)

The top left vertex is (0,a) as shorter side of the rectangle is half the length of the longer side.

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If the perimeter of the rectangle is given, then we can find the sum of all sides, which is 2 times the length plus 2 times the width.

Perimeter = 2l + 2w = 2(6w) + 2w = 14w

Given perimeter = 28

So, 14w = 28, which means w = 2. Then, l = 6w = 12.

Therefore, the area of the rectangle is A = l x w = 12 x 2 = 24 square units.

To find the area of a rectangle, we need to know both the length and width. In this case, we are given a relationship between the length and the width of the rectangle. Specifically, the length is six times the width, or l = 6w.

We are also given the perimeter of the rectangle. The perimeter is the sum of all four sides of the rectangle, which is 2 times the length plus 2 times the width. So, we can write:

Perimeter = 2l + 2w

Substituting l = 6w, we get:

Perimeter = 2(6w) + 2w = 14w

We are told that the perimeter of the rectangle is 28, so we can set 14w equal to 28 and solve for w:

14w = 28

w = 2

Once we know the value of w, we can find the value of l:

l = 6w = 6(2) = 12

Now that we know both the length and the width, we can calculate the area of the rectangle:

A = l x w = 12 x 2 = 24

Therefore, the area of the rectangle is 24 square units.

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When testing the hypotheses H0: μ ≥ 100 and Ha: μ < 100 at a level of significance α, the null hypothesis will be rejected if the test statistic z is less than -zα.

In hypothesis testing, the test statistic z measures how many standard deviations the sample mean is away from the hypothesized population mean under the null hypothesis. The critical region for the alternative hypothesis Ha: μ < 100 is in the left tail of the standard normal distribution.

To reject the null hypothesis H0: μ ≥ 100, the test statistic z must fall in the critical region. Since the alternative hypothesis is μ < 100, we want the test statistic to be significantly lower than the critical value.

The critical value for a one-tailed test at a level of significance α is denoted by -zα, representing the value below which we reject the null hypothesis. Therefore, if the test statistic z is less than -zα, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Option b, which states that the test statistic z is less than -zα, is the correct answer.

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Answer:

The answer is 6

Step-by-step explanation:

60-36-18=6

The value of "x" in the given figure and question is 20 units.

As per the question statement, We are given a figure in which we are supposed to find the value of x.

Before solving the question, if we observe the figure, we can conclude that this question will include the concepts of right angled triangle or specifically Pythagoras Theorem, which states that

\(Perpendicular^{2} + base^{2} = hypotenuse^{2}\) where perpendicular, base and hypotenuse are the three sides of the right angled triangle.

In Triangle RTQ

using Pythagoras Theorem

\(RQ^{2} = TQ^{2} +TR^{2} \\RQ=x\\x^{2} = 16^{2} + TR^{2} \\TR^{2} = x^{2} -16^{2}\)

Now considering triangle SRT

using Pythagoras Theorem

\(SR^{2} = RT^{2} + ST^{2} \\SR^{2} = (x^{2} -16^{2}) +9^{2}\\\)

Now considering triangle RSQ

using Pythagoras Theorem

\(SQ^{2} = SR^{2} +RQ^{2} \\(9+16)^{2} = SR^{2} + RQ^{2} \\(9+16)^{2} = x^{2} -7^{2}+x^{2} \\ (9+16)^{2} =2x^{2} -7^{2} \\25^{2}+7^{2} = 2x^{2}\)

\(2x^{2} =674\)

\(x^{2} =337\\x=\sqrt{337} \\x=18.357\)

Therefore x = 18.357 approx 20 units.

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Step-by-step explanation:

All inputs either point to 1 or 6 so the range is 1,6

Answer:

Weight Calculator

Standard conversion factors.

1) MILD STEEL (MS)

MS SQUARE. WEIGHT (KGS ) = WIDTH X WIDTH X 0.00000785 X LENGTH. ...

MS ROUND. WEIGHT (KGS ) = 3.14 X 0.00000785 X ((diameter / 2)X( diameter / 2)) X LENGTH. ...

SS ROUND. DIA (mm) X DIA (mm) X 0.00623 = WEIGHT PER METRE. ...

SS / MS CIRCLE. ...

SS sheet. ...

S.S HEXAGONAL BAR.

Step-by-step explanation:

Therefore, the average rate of change over the interval [−5, 10] for the function g(x) = log2(x^6) − 3 is -16/5.So, the correct option is (none of these).Answer: (none of these)

The given function is g(x) = log2(x^6) − 3 and we are to find the average rate of change over the interval [−5, 10].To find the average rate of change of the function g(x) over the interval [a, b], we use the following formula:average rate of change = (f(b) - f(a))/(b - a)where f(a) and f(b) are the values of the function at the endpoints of the interval [a, b].Hence, the average rate of change of the function g(x) over the interval [−5, 10] is given by:average rate of change = (g(10) - g(-5))/(10 - (-5))We now need to evaluate g(10) and g(-5).We have g(x) = log2(x^6) − 3Putting x = 10, we get:g(10) = log2(10^6) − 3 = 6log2(10) − 3Putting x = -5, we get:g(-5) = log2((-5)^6) − 3 = log2(15625) − 3Thus,average rate of change = (6log2(10) − 3 − (log2(15625) − 3))/(10 - (-5))= (6log2(10) − log2(15625))/15= (6 log2(10/15625))/15= (6 log2(2/3125))/15= (6 (-8))/15= -48/15= -16/5

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The option that represents the average rate of change over the interval [−5, 10] for the function g(x) = \(log2(x^6) − 3\) is  -0.4194.

We are to determine the average rate of change over the interval [−5, 10] for the function,

g(x) = \(log2(x^6) − 3.\)

The average rate of change is defined as the ratio of the change in y to the change in x.

It is the slope of the line that contains the endpoints of the given interval.

We are given that g(x) = \(log2(x^6) − 3\) and we want to find the average rate of change of this function over the interval [−5, 10].

We have the following formula to find the average rate of change over an interval for a function:

\(\frac{g(b)-g(a)}{b-a}\)

Where a and b are the endpoints of the interval.

Here, a = -5 and b = 10.

We have:

g(a) = g(-5)

= \(log2[(-5)^6] - 3\)

= log2[15625] - 3

≈ 9.291

g(b) = g(10)

= \(log2[10^6] - 3\)

= 6 - 3

= 3

Therefore, the average rate of change of g(x) over the interval [-5, 10] is given by:

\(\frac{g(b)-g(a)}{b-a}=\frac{3-9.291}{10-(-5)}\)

=\(\frac{-6.291}{15}\)

=\(\boxed{-0.4194}\)

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Answer:

From what I see, the answer is graph D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Part a:  10z > 25,670; infinite integer.

Part b: Range =  2550 to 2649.

Part a:  10z > 25,670

Divide the inequality on both sides by 10.

z >  2,567

Thus, there are infinite number which are greater than 2567.

Part b:  z rounded to the nearest hundred is 2,600.

Range =  2550 to 2649.

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Answer:

4.36 to 4.46

good luck buddy

Plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3) on graph as below.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

The given linear equation is y= -1.5x.

Substitute, x=0, 1, 2, 3, 4, 5, .......

So, y=0, -1.5, -3, -4.5, -6.0, ....

Plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3)

Therefore, plot the coordinate points (0, 0), (1, -1.5), (2, -3.0), (-1, 1.5) and (-2, 3) on graph as below.

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"Your question is incomplete, probably the complete question/missing part is:"

Graph linear equations y= -1.5x.

Answer:

Its A and D

Step-by-step explanation:

Trust me ;)

The population of the town in 1960 is 48.80 thousands

The equation of the model is given as:

f(t) = 42e^(0.015t)

1960 is 10 years after 1950.

This means that:

t = 10

Substitute t = 10 in f(t) = 42e^(0.015t)

f(10) = 42e^(0.015 * 10)

Evaluate

f(10) = 48.80

Hence, the population of the town in 1960 is 48.80 thousands

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Answer:

The number of different ways the car can be built is 31 different ways

Step-by-step explanation:

The given options are'

1), Leather seats, 2) Heated seats, 3) Sunroof, 4) Tinted windows, 5), back up camera

Therefore, the number of different ways the car can be built, n, is given as follows;

n = ₅C₁  + ₅C₂ + ₅C₃ + ₅C₄ + ₅C₅

n = 5 + 10 + 10 + 5 + 1 = 31 different ways

The number of different ways the car can be built = n = 31 different ways

Given:

defective units = 29.1

total production = 9,700

Hence:

substituting values in the formula:

ANSWER

0.3 percent of the production is defective.

Answer:

She need \(\frac{1}{4}\) cups of corn.

Step-by-step explanation:

Libby needs to make \(\frac{1}{2}\) of her chilli recipe for the school's chilli contest. If Libby usually need \(\frac{1}{2}\) cup of corn for her recipe.

She make half of her recipe

So, we can set up equation for unknown corn she need for the chilli contest as 'x' cups

\(\frac{1}{0.5} =\frac{0.5}{x}\)

Cross multiply

x=0.25

To make it as a fraction, she need \(\frac{1}{4}\) cups of corn.

Answer:

yep 1/4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

There's nothing to answer to that question, can you be specific.

Step-by-step explanation:

Answer:

x = -5

Step-by-step explanation:

-4x + -3 = 17

-4x - 3 = 17

-4x - 3 + 3 = 17 + 3

-4x = 20

-4x/-4 = 20/-4

x = -5

Hope this helps!

Answer:

x=-5

Step-by-step explanation:

-4x+-3=17

First add 3 to both sides.

-4x=20

Then divided by -4

Note: Negatove divided by postive is negative.

20÷(-4) = -5

So.

x=-5

The angles in the triangle are as follows;

∠1 = 41°

∠2 = 85°

∠3 = 95°

∠4 = 85°

∠5 = 36°

∠6 = 49°

∠7 = 57°

When line intersect each other, angle relationships are formed such as vertically opposite angles, linear angles etc.

Therefore,

∠2 = 180 - 95 = 85 degree(sum of angles on a straight line)

∠1 = 360 - 90 - 144 - 85 = 41 degrees (sum of angles in a quadrilateral)

∠3 = 95 degrees(vertically opposite angles)

∠4 = 85 degrees(vertically opposite angles)

∠5 = 180 - 144 = 36 degrees (sum of angles on a straight line)

∠6 = 180 - 36 - 95 =49 degrees (sum of angles in a triangle)

∠7 = 180 - 38 - 85 = 57 degrees (sum of angles in a triangle)

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The link represented by function g multiplies the dependent variable by 9 for every increase of 2 units in the independent variable. The equation that represents g is \(g(x)= 2 \times3^x\),and the function has a value of 2 at 0

Let x be the independent variable, and let g(x) be the dependent variable.

According to the problem, for every 2 units the independent variable increases, the dependent variable is multiplied by 9. This suggests an exponential relationship of the form:

 \(g(x)= a \times b^x\)

where a is the initial value of the dependent variable (when x=0), and b is the growth factor (how much the dependent variable changes for every unit increase in x).

We are given that g(0) = 2, so we can plug in these values and solve for a:

 \(g(0)= a \times b^0\)

a = 2

So now we have:

\(g(x)= 2 \times b^x\)

We still need to find the growth factor b. We are told that the dependent variable is multiplied by 9 for every 2 units the independent variable increases. In other words:

\(g(x+2) = 9 \times g(x)\)

Using our equation for g(x), we can substitute in and simplify:

  \(2 \times b(x+2) = 9 \times 2\times b^x\)

Simplifying, we get:

\(b^2\) = 9

Taking the square root of both sides (we take the positive square root since b must be positive in order for g to be an increasing function), we get:

b = 3

So the final equation for g(x) is:

\(g(x) = 2 \times 3^x\)

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