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How can you make a 95% confidence interval smaller without changing the confidence level?

I NEED EXPLANATION

Answer:

$275

Step-by-step explanation:

If you multiply 24 by 15 you get the total which is $360. When you subtract the $85 he spent you get $275 left over that he is saving.

Answer:

Hope this helps ;)

Step-by-step explanation:

To find the time it takes the T-shirt to reach its maximum height, we need to find the value of t when the velocity of the T-shirt is zero, because at this point the T-shirt has reached its maximum height and starts falling back down. We can find the velocity of the T-shirt by taking the derivative of the height equation with respect to time:

v(t) = h'(t) = 72

The velocity of the T-shirt is a constant 72 feet per second, so it will never reach a velocity of zero and will never reach its maximum height. The T-shirt will keep going up indefinitely.

If the problem had specified that the T-shirt was launched with an initial upward velocity of -72 feet per second (meaning it was launched downward), then we could have found the time it takes the T-shirt to reach its maximum height by setting v(t) = 0 and solving for t. In this case, we would find that t = 1, so it would take the T-shirt 1 second to reach its maximum height. The maximum height would be h(1) = -16 + 72(1) + 6 = 62 feet.

A function is a relationship between inputs where each input is related to exactly one output.

The value of \(h^{-1}(x)\) is (x -5)/5

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

h(x) = 5x + 2

To find \(h^{-1}(x)\).

Step 1: Keep h(x) = y.

Step 2: Replace y with x and x with y.

Step 3: Solve for y.

Step 4: Change y = \(h^{-1}(x)\)

Now,

y = 5x + 2

x = 5y + 2

x - 2 = 5y

(x - 2) / 5 = y

y = (x - 2) / 5

\(h^{-1}(x)\) = (x -2) / 5

Thus,

The value of \(h^{-1}(x)\) is (x -5)/5

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Answer:

The answer is B formal

Answer:

B on edge 2021

Step-by-step explanation:

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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Answer:

5

Step-by-step explanation:

3(2x+1)=7x-2

6x + 3 = 7x - 2

6x - 7x = -2 - 3

-x = -5 /(-1)

x = 5

Answer:

5

Step-by-step explanation:

3 ( 2x + 1 ) = 7x - 2

Step 1 : Remove the parentheses

6x + 3 = 7x - 2

Step 2 : Move the variable to the left-hand side and move extra number the right-hand side

6x + 3 = 7x - 2

-7x  -3   -7x  -3

6x - 7x = -2 - 3

Step 3 : Combine like terms

-x = -5

Step 4 : Change the sign to make x positive

x = 5

SOLUTION : x = 5

Hope this helps :)

Answer:

The number of innings Brantley pitched is 7.

Step-by-step explanation:

We are given that the table shows the number of innings pitched by each of the Greenbury Goblins' starting pitchers during the Rockbottom Tournament below;

         Pitcher                           Number of innings pitched

          Calvin                                            11

          Thom                                             12

          Shawn                                            7

            Kris                                               3

         Brantley                                           x

Let the number of innings Brantley pitched be 'x'.

The mean of the following data set is given by the following formula;

          Mean = \(\frac{\text{Sum of all data values}}{\text{Total number of observations}}\)

                  \(8 = \frac{11+12+7+3+x}{5}\)

                 \(8\times 5 =33+x\)

                 \(40 = 33+x\)

                  x = 40 - 33 = 7

Hence, the number of innings Brantley pitched is 7.

Answer:

7

Step-by-step explanation:

Khan Academy

Answer:

it's B

Step-by-step explanation:

9wcbux2v9wcuuv9w9uve2cu92cveu02x0v2xuv2uh wce

Answer:

94.25 kg I think

Step-by-step explanation:

58/4 =14.5 kg per bushel

6.5 x 14.5=94.25 kg

Answer:

94.25

Step-by-step explanation:

First you need to find the unit rate which is 58/4 which equals to 14.5 then you multiply by 6.5 to find 94.25

Answer:

30 i think

Step-by-step explanation:

The values of the probabilities are  3.59%,  19.27%, 8.50% and 0.125

3 adults at random

From the pie chart, we have

None = 33%

For three selections, we have

P(None) = (33%)^3

P(None) = 3.59%

6 adults at random

From the pie chart, we have

None = 33% and All = 43%

For six selections, we have

P(Not Some) = (43% + 33%)^6

P(Not Some) = 19.27%

4 adults at random

From the pie chart, we have

None = 33% and Some = 21%

For four selections, we have

P(Not Few) = (21% + 33%)^4

P(Not Few) = 8.50%

Here, we have

Total = 40

Numbers = 5

So, we have

P(Win) = 5/40

P(Win) = 0.125

Hence, the probability of winning is 0.125

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To answer this question, we need to compare the ratios of miles traveled to gallons of gas used for car A and car B when they both use 1 gallon of gas.

For car A, we can see from the graph that 50 miles are traveled for every 2 gallons of gas used, or in other words, 25 miles are traveled for every 1 gallon of gas used. Therefore, car A can travel 25 times the distance for 1 gallon of gas.

For car B, we can see from the table that 40 miles are traveled for every 2 gallons of gas used, or in other words, 20 miles are traveled for every 1 gallon of gas used. Therefore, car B can travel 20 times the distance for 1 gallon of gas.

To compare the two ratios, we can divide the ratio of miles traveled to gallons of gas used for car A by the ratio for car B:

25/20 = 1.25

Therefore, car A can travel 1.25 times the distance car B can travel when both cars use 1 gallon of gas.

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

Answer:

As base and height are becoming double the new area is 4 times the original area. When the length of the sides of a triangle double, the area becomes quadruple.

Answer:6 pens are blue

Step-by-step explanation:because 14-8=6 pens would be left and would be blue

Answer:

y = 8 because both of the circle is same.

212/351

or

211/351

cos less than

The subtotal before the surcharge and sales tax is $12.2

In this question, we have the following parameters

Total = $13.73

Sales tax = 4%

Surcharge = $1

The above parameters imply that:

Total = Subtotal * (1 + sales tax) + Surcharge

Substitute the known values in the above equation, so, we have the following representation

13.73 = Subtotal * (1 + 4%) + 1

This gives

Subtotal * (1 + 4%) = 12.73

Divide both sides by 1.04

Subtotal = 12.2

Hence, the subtotal is $12.2

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The graph of y = 3 x 2^x passes through the coordinate points (2,12) and (3,24).

To write a question in the form of y=a x b^x that passes through the coordinate points (2,12) and (3,24), we need to solve for the values of a and b.

First, let's substitute the coordinates (2,12) into the equation:
12 = a x b^2

Next, let's substitute the coordinates (3,24) into the equation:
24 = a x b^3

We now have two equations with two unknowns (a and b), which we can solve using algebra.

From the first equation, we can solve for a:
a = 12 / b^2

We can then substitute this value of a into the second equation:
24 = (12 / b^2) x b^3

Simplifying this equation, we get:
2 = b

We can then substitute this value of b back into the equation for a:
a = 12 / 2^2
a = 3

Therefore, the equation of the graph that passes through the coordinate points (2,12) and (3,24) is:
y = 3 x 2^x

We can check that this equation is correct by plugging in the coordinates:
When x = 2: y = 3 x 2^2 = 12
When x = 3: y = 3 x 2^3 = 24
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The value of the function operation f - g(x) is 3x² + x

Function operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.

Addition and subtraction of functions:

A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.

Multiplication of functions:

Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.

Composition of functions:

Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.

In this problem, we have two functions which are;

The value of (f - g)(x) = 3x² + x

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Therefore , the solution of the given problem of function comes out to be the interval's edges, rounded to four decimals, are -1.3233 and 0.7838.

The math lesson includes a variety of subjects, such as math, integers, but one's subdivisions, as well as architecture, construction, and that both real but rather fictitious geographic locations. A work covers the connections between different variables that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinctive results for each input.

Here,

First, we assess f(x) at the interval's endpoints:

=> f(-3) = 2(-3)^3 - 7(-3) + 4 = -43

=> f(3) = 2(3)^3 - 7(3) + 4 = 44

There must be at least one root in each of the gaps between (-3, r) and (r, 3), where r is the function's root, because the function changes sign at x = -3 and x = 3. To find the function's roots numerically,

we can use the bisection technique or Newton's method.

We can plot the function using a graphing calculator or computer software and see that there is one root in the range (-3, -2), one root in the range (-2, 0), and one root in the range (-3, -2). (0, 3).

Consequently, the periods where the function is positive on the range (-3, 3) are as follows:

=> (-3, -1.3233) and (0.7838, 3) (0.7838, 3)

The interval's edges, rounded to four decimals, are -1.3233 and 0.7838.

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The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Answer:

8+x , x+8

Step-by-step explanation:

5+3 =8
x cannot be simplified since its value is unknown.
8+x or x+8

Answer:

x+8

Step-by-step explanation:

First, combine like terms

5+3=8

(x+8)

See explanation below

Explanation:

Given expression: x² + 4x + 1

For the above expression to be factored, we need to have two numbers that can be added together to give 4 and the product of those number to give 1

For a quadratic expression: ax² + bx + c

a = 1, b = 4, c = 1

there are no factors where the addition of both numbers give b = 4 and the product of those number give 1.

Also, we can apply the formula: b² = 4ac to determine if we can factorise wihout getting complex root or decimals. When we factor, we get only whole numbers, no decimals.

4² = 4(1)(1)

16 = 4

We can see the above contradict it self as 16 is no equal to 4

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

Sequences are series of elements generated according to at least one condition, usually equations. geometric sequences are generated according to a exponential formulas, whose form and characteristics are described below:

f(n) = a · bⁿ ⁻ ¹    (1)

Where:

If we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:

f(12) = 4 · 2¹² ⁻ ¹

f(12) = 4 · 2¹¹

f(12) = 4 · 2,048

f(12) = 4,096

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

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We got x = 16.54 by using Pythagorean theorem .

What is the Pythagorean theorem in plain English?

angle of semicircle is always be 90° .

   18² = 7.1² + x²

    324 = 50.41 + x²

     x² = 324 - 50.41

          = 273.59

    x = √ 273.59

    x = 16.54

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Answer:

\(\boxed{\sf C. \ x\geq -4}\)

Step-by-step explanation:

\(-8x+4\leq 36\)

\(\sf Subtract \ 4 \ from \ both \ sides.\)

\(-8x+4-4 \leq 36-4\)

\(-8x\leq 32\)

\(\sf Divide \ both \ sides \ by \ -8.\)

\(\frac{-8x}{-8} \leq \frac{32}{-8}\)

\(x\geq -4\)

Answer: 1,200.65+ 985.43+ 1,200.23= 3,386.31

Step-by-step explanation:

The x-coordinate of the vertex is given by h = -2 and the equation of the axis of symmetry is x = -2.

Given function is H(x) = -(x + 2)² + 8.

The axis of symmetry of a quadratic function y = ax² + bx + c is defined by x = -b/2a.

So, let's solve the problem as follows:

To find the axis of symmetry, we need to convert the given function into standard form y = a(x - h)² + k.

We can do this by completing the square.

For that, we have

H(x) = -(x + 2)² + 8H(x)

= -1(x² + 4x + 4) + 8H(x)

= -1(x + 2)² + 8

The standard form is y = a(x - h)² + k, so the given function is y = -1(x + 2)² + 8.

The vertex form of a quadratic equation is y = a(x - h)² + k

Where(h, k) is the vertex.

The vertex form of the given function H(x) = -(x + 2)² + 8 can be calculated as follows:  

y = a(x - h)² + k

The vertex form is y = a(x - h)² + k.

Where the vertex form of the given function is:

y = -1(x + 2)² + 8.

Since the vertex form is y = a(x - h)² + k the vertex form of the given function is y = a(x + 2)² + 8 and (h, k) = (-2, 8).

Vertex is given by h = -2.

Axis of symmetry is x = -2.

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Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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