The graph of an equation is sketched in the figure.
Describe five ordered-pair solutions of this equation by
using a table.
X
-6
-3
0
3
6
y
☐
I
8-
10-88427
6
40
10

The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is  (9.7, 14.7).

Here, we have,

1. Identify the given information:

 - Confidence level (c) = 0.95

 - Sample mean (x) = 12.2

 - Sample standard deviation (s) = 3.0

 - Sample size (n) = 8

2. Determine the degrees of freedom (df) for the t-distribution:

 - df = n - 1 = 8 - 1 = 7

3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:

 - You can use a t-table or an online calculator for this.

 - The t-value for a 0.95 confidence level and 7 df is approximately 2.365.

4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):

 - ME = t-value * (s / sqrt(n))

 - ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5

5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):

 - Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7

 - Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7

So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).

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Answer:

64.14

Step-by-step explanation:

Reading the passage I see that you have to multiply then divide

The surface area of the larger solid is,  171.7 mm²

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The volumes of two similar solids are 857.5 mm³ and 540 mm³.

And, The surface area of the smaller solid is 108 mm².l

Now, Let us assume that;

The surface area of the larger solid is, x

Hence, We get;

857.5 / x = 540 / 108

Solve for x as;

857.5 x 108 = 540 x

92,718 = 540x

x = 171.7 mm²

Thus, The surface area of the larger solid is,  171.7 mm²

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Answer:10-x

Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.

The graph seems to be a left symmetrical distribution and most people watched action movies

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

From the graph, we have the following readings and observations

Using the above as a guide, we have the following conclusions

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The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis

The ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.

If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).

If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).

The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.

Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.

Solving the given problem:

f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]

At x= 0 on the y- axis

f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]

Thus, only option C satisfies this condition.

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Answer:

The heights and shadows of the objects are legs of similar right triangles. We can use these similar triangles to set up a proportion to solve for the height of the building.

2.9 / 1.26 = x / 47.25

x = 108.75 m

Andy has $32 money left after spending $18 on school supplies and $47 on new clothes.

To find out how much money Andy has left, we need to start with the total amount of money he saved and then subtract the amount he spent on school supplies and new clothes.

The total amount Andy saved is:

$32 + $27 + $38 = $97

The amount Andy spent is:

$18 + $47 = $65

To find out how much money Andy has left, we can subtract the amount he spent from the amount he saved:

$97 - $65 = $32

So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.

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Carlos can expect the value of the computer to be $580 three years after purchase.

To model the value of the computer, we can use the formula:

y = abˣ

We know that the initial value of the computer is $1,350, so a = 1350.

We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:

810 = 1350b

b= 0.6

b = 0.6

So our exponential equation is:

y = 1350(0.6)ˣ

To find the value of the computer 3 years after purchase, we can substitute x = 3:

y = 1350(0.6)³

y = 583

Hence, Carlos can expect the value of the computer to be $580 three years after purchase.

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Answer: 97.5

Step-by-step explanation:

Just do base times height divided by 2, which I'm assuming is 13x15 , that'd be 195. 195 divided by 2 is 97.5

Answer:

240 8018

Step-by-step explanation:

two hundred forty eight thousand and eighteen

The smallest fraction is 8/12, which is equivalent to 2/3.

To compare fractions, it's best to convert them all to a common denominator.

3/4 is equivalent to 9/12

2/3 is equivalent to 8/12

10/12 is equivalent to 5/6

2/1 is equivalent to 24/12

So, the smallest fraction is 8/12, which is equivalent to 2/3.

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To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.

How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.

For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:

V = l × w ×h

The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.

Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.

V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.

We arrive at a total volume of 792 cubic meters by adding these volumes together.

To the nearest hundredth=904.600 cubic meters.

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The ratio of true positives to false positives, given the accuracy of the test would be 239 : 711 .

Here. we have,

First, find the number of people who have the flu:

= 5. 2 % x 10, 000

= 520 people

Those who don't have it:

= 10, 000 - 520

= 9, 480 people

True positive :

= 92 % x 520

= 478 people

False negatives:

= 8 % x 520

= 42 people

False positives:

= 15 % x 9, 480

= 1, 422 people

The ratio of true positives to false positives is therefore:

478 : 1, 422

239 : 711

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Answer:

2 (n - 3) (n - 6)

Step-by-step explanation:

[tex]-7n+5n^2+6-3n^2-11n+30[/tex]

Group like terms and combine...

[tex]2n^2-18n+36[/tex]

Observe that all terms contain a factor of 2.  Factor out a 2...

[tex]2(n^2-9n+18)[/tex]

The leading coefficient is 1.  The shortcut applies.  Find the factors of "c" (18)

Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").

Finish factoring the trinomial into two binomials:

[tex]2(n-3)(n-6)[/tex]

To verify that this is a valid factoring, distribute, and recombine terms:

[tex]2(n-3)(n-6)[/tex]

[tex]2(n^2-3n-6n+18)[/tex]

[tex]2(n^2-9n+18)[/tex]

The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as  51 square units.

A graph is described as a mathematical representation of a network and it describes the relationship between lines and points.

The first step is to divide the figure is into two rectangles and a triangle.

we notice that the points B, C, E, and F will form a rectangle with base BC and height of 7 units.

We also notice that the  points A, D, and G form a rectangle with base AG and height 5 units.

we notice that  points C, D, and E form a triangle with base CE and height 4 units.

we notice that the  length of BC is 4 - 4 = 0, therefore  the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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Answer:



Step-by-step explanation:

Therefore, 70% of state capitals do not have interstate highways serving them.

Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.

Here,

If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.

To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:

84 / 120 x 100% = 70%

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The number of kg of maize was left with Ali is 73350 Kg.

Given that, Ali had 3469 bags of maize each weighing 90 kg.

Ali sold 2654 of them.

Number of bags left = 3469-2654

= 815

Number of Kg's of maize left = 815×90

= 73350 Kg

Therefore, the number of kg of maize was left with Ali is 73350 Kg.

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Answer:

24.6%

Step-by-step explanation:

denote B: bad mood; H: healthy; D: periodontal disease

P(B|D)

=P(B,D) / P(D)

=P(B,D) / [P(D,B)+P(D,H)]          ### law of total probability ###

=P(D|B)P(B) / [P(D|B)P(B) + P(D|H)P(H)]

=(0.85)*(0.1)/[(0.85)*(0.1) + (0.29)*(0.9)]

=0.245664739

Answer:

Step-by-step explanation:

The margin of error represents the range of values within which the true population mean is likely to fall with a certain level of confidence. To calculate the range of values for the actual mean number of hours spent in meetings in a week, we can use the formula:

(actual mean) = (sample mean) ± (margin of error)

Substituting the given values, we get:

(actual mean) = 4.3 ± 1.1

To find the range of values, we need to compute the upper and lower bounds of this interval:

Lower bound = 4.3 - 1.1 = 3.2 hours

Upper bound = 4.3 + 1.1 = 5.4 hours

Therefore, the actual mean number of hours spent in meetings in a week is between 3.2 and 5.4 hours.

The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.

In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:

h(t) = 60 · t - 5 · t²

Where:

We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:

30 = 60 · t - 5 · t²

6 = 12 · t - t²

t² - 12 · t + 6 = 0

(t - 11.477) · (t - 0.523) = 0

t = 11.477 s. or t = 0.523 s.

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Answer:

5.6 mi

Step-by-step explanation:

1 km is around 0.6 (estimate) miles so just multiply both sides by 9 and 9km = around 5.4 miles and 5.6 is the closest so it is most likely that

Note that the five number summary and range for the data are given as follows:

The five-number summary and range were calculated using the given stem and leaf plot. The minimum value is 102, the first quartile (Q1) is 226, the median (Q2) is 340, the third quartile (Q3) is 492, and the maximum value is 670. The range is the difference between the maximum and minimum values, which is 568.

The range is calculated by subtracting the minimum value from the maximum value:

Range: 607 - 102 = 505

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The square cake can be distributed in such a way that each person out of 15 guest may get 8  , with the least amount left over .

The Correct option is (1).

What is Volume of any shape?

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.

First find the volume of square cake,

Volume = l x b x h

= 8 x 8 x 2

=128

Now there are total 15 guests, Each of get

=

=  8.533

2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)

Volume=

=

=

=28.26  

Now there are total 15 guests, Each of get

=

= 1.884

3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)

Volume=

=

=

=50.24  

Now there are total 15 guests, Each of get

=

=  3.349

4. Volume = l x b x h

= 6 x 9 x 2

=108

Now there are total 15 guests, Each of get

=

=  7.2

According to question each person may get 8 .

Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .

Answer:

Step-by-step explanation:

Answer: 18.75

Step-by-step explanation:

small greeting cards = 1.80

large greeting cards = 3.85

1.80 x 4 = 7.20

3.85 x 3 = 11.55

7.20 + 11.55 = 18.75