Evaluate and match each expression on the left to its valueon the right, when x = 7 and y = 4.

Answer:

4.6 hours

Step-by-step explanation:

we first need to calculate the total distance he covered and total time taken whole for the journey.

Distance= speed X time

time = Distance/speed

let the total distance be X. he covers 2/5 if the journey first.

2/5 = 0.4

Time = 0.4x/45 hours

the remaining journey is 3/5x

he covers 1/3 X 3/5= 0.2x

time taken = 0.2/90 X hours

the remaining distance = 100× 1.2 = 120km

we add 0.4x + 0.2x to get the fraction he had covered

0.6x.

the remaining distance was X - 0.6x = 0.4 X

thus 120 km represents 0.4x of the journey

we calculate now the value of X

0.4x = 120

X = 300km

Total time taken = 0.4x/45 + 0.2/90 + 1.2 hours

replace X to get time

2.7 hours + 0.7 hours + 1.2 hours

= 4.6 hours

The probability that the next customer will pay with a debit card or a credit card is 12%.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the next customer would pay with a debit card or a credit card = (number of customers that paid with a debit card + number of customers that paid with a credit card) / total number of customers

(8 + 2)/ 83 = 0.12 = 12%

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Answer: 48 red beads

Step-by-step explanation:

3 red beads: 1 bracelet

16 bracelets * 3 read beads/1 bracelet=

16*3/1=

16*3=48 red beads

Answer:

64 miles per gallon

27 feet per second

14 quarts in a barrel

Step-by-step explanation:

The 90% confidence interval for the given data is 4.8 ± 2.73.

A confidence interval is a type of interval computation used in statistics that determines the true value of an unknown parameter based on the observed data. The interval estimates the deterministic parameter with a level of confidence that is quantified by the confidence level.

Given, sample mean (x) = 4.8

           z at 90% confidence level = 1.645

           sample standard deviation (s) = 5.25

           sample size (n) = 10

We know that, Confidence interval = x ± (z × s) ÷ √n

                                                           = 4.8 ± (1.645×5.25)/√10

                                                           = 4.8 ± 8.63625/3.1622

                                                           = 4.8 ± 2.73

            ∴ Lower bound = 4.8 - 2.73 = 2.07

       and, Upper bound = 4.8 + 2.73 = 7.53

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Answer:

A square pyramid has 5 faces: 1 square base and 4 triangular faces.

The area of the base is:

A = s^2

where s is the length of the base edge.

In this case, s = 1 m, so:

A = 1^2 = 1 m^2

The area of each triangular face is:

A = 1/2 * b * h

where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).

In this case, b = 1 m and h = 1 m, so:

A = 1/2 * 1 * 1 = 0.5 m^2

The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:

SA = A_base + 4 * A_triangles

SA = 1 + 4(0.5)

SA = 1 + 2

SA = 3 m^2

Therefore, the surface area of the pyramid is 3 square meters.

Answer:

I think that it might be a type-o on the assignment. If I was you I would email your teacher.

The equation of f(x) include the following: A. f(x) = (x - 5)² - 2.

In Mathematics and Geometry, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Next, we would create a system of equation by using the data points provided in the table above;

a(3)² + b(3) + c = 2

9a + 3b + c = 2    .....equation 1.

a(0)² + b(0) + c = 23

c = 23    .....equation 2.

a(1)² + b(1) + c = 14

a + b + c = 14    .....equation 3.

By solving the system of equations simultaneously, the values of a, b, and c are as follows;

a = 1

b = -10

c = 23

Therefore, the required quadratic function in vertex form is given by;

ax² + bx + c = 0

x² - 10x + 23 = 0

f(x) = x² - 10x + 23

f(x) = (x - 5)² - 2

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The probability that the number of tails obtained is between 3 and 7 is

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space/ total possible outcome

if a coin is tossed 8 times, the total outcome is 8×2 = 16

probability that head comes 3 times = 1×3 /16= 3/16

probability that head comes out 7times = 7/16

therefore the probability that head comes out between 3 times and 7 times

= 3/16 × 7/16

= 21/256

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The length of wire used for the equilateral triangle is approximately 5.61 meters.

The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.

Here,

To minimize the total area of both figures, we need to find the optimal cut point for the wire.

Let's assume the length of the wire used for the equilateral triangle is x meters, and the remaining length of the wire used for the circle is (9 - x) meters.

For the equilateral triangle:

An equilateral triangle has all three sides equal in length.

Let's call each side of the triangle s meters. Since the total length of the wire is x meters, each side will be x/3 meters.

The formula to find the area of an equilateral triangle with side length s is:

Area = (√(3)/4) * s²

Substitute s = x/3 into the area formula:

Area = (√(3)/4) * (x/3)²

Area = (√(3)/4) * (x²/9)

Now, for the circle:

The circumference (perimeter) of a circle is given by the formula:

Circumference = 2 * π * r

Since the remaining length of wire is (9 - x) meters, the circumference of the circle will be 2π(9 - x) meters.

The formula to find the area of a circle with radius r is:

Area = π * r²

To find the area of the circle, we need to find the radius.

Since the circumference is equal to 2πr, we can set up the equation:

2πr = 2π(9 - x)

Now, solve for r:

r = (9 - x)

Now, substitute r = (9 - x) into the area formula for the circle:

Area = π * (9 - x)²

Now, we want to minimize the total area, which is the sum of the areas of the triangle and the circle:

Total Area = (√(3)/4) * (x²/9) + π * (9 - x)²

To find the optimal value of x that minimizes the total area, we can take the derivative of the total area with respect to x, set it to zero, and solve for x.

d(Total Area)/dx = 0

Now, find the critical points and determine which one yields the minimum area.

Taking the derivative and setting it to zero:

d(Total Area)/dx = (√(3)/4) * (2x/9) - 2π * (9 - x)

Setting it to zero:

(√(3)/4) * (2x/9) - 2π * (9 - x) = 0

Now, solve for x:

(√(3)/4) * (2x/9) = 2π * (9 - x)

x/9 = (8π - 2πx) / (√(3))

Now, isolate x:

x = 9 * (8π - 2πx) / (√(3))

x(√(3)) = 9 * (8π - 2πx)

x(√(3) + 2π) = 9 * 8π

x = (9 * 8π) / (√(3) + 2π)

Now, we can calculate the value of x:

x ≈ 5.61 meters

So, the length of wire used for the equilateral triangle is approximately 5.61 meters.

The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.

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The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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Answer:

$132

Step-by-step explanation:

Hope this helps!

Answer:

The answer is likley 6/9

Step-by-step explanation:

Total number of balls = 9

Red: 3/9 chance of being selected

Green: 6/9 chance of being selected

Basically, there is a way higher chance of selecting 3 green balls and an even HIGHER chance of selecting 6!

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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The standard form of the equation of the parabola with a focus of (4, -3), and a directrix of x = 0 is; (y + 3)² = 8·(x - 2)

The equation of a parabola with a focus (4, -3) and a directrix of x = 0, can be found using the definition of the curve of a parabola, which is a curve that describes the location of a point that is equidistant from the focus and the directrix.

Let (x, y) represent the coordinate of the point, therefore;

The distance of the point from the point to the focus is therefore;

Distance = √((x - 4)² + (y + 3)²)

The distance from between the point and the directrix = |x|

According to the definition of the locus of a parabola, therefore;

√((x - 4)² + (y + 3)²) = |x|

(x - 4)² + (y + 3)² = x²

x² + y² - 8·x + 6·y + 25 = x²

x² - x² + y² - 8·x + 6·y + 25 = 0

y² - 8·x + 6·y + 25 = 0

y² + 6·y + 25 = 8·x

However, we get; Directrix, x = h - p

focus = (h + p, k)

Therefore;

h + p = 4

k = -3

h - p = 0

2·h = 4 + 0 = 4

h = 4/2 = 2

h = 2

p = 4 - 2 = 2

p = 2

The equation of a parabola is; (y - k)² = 4·p·(x - h)

The equation of the parabola is; (y - (-3))² = 4 × 2 × (x - 2)

The standard form of the equation is therefore;

(y + 3)² = 8·(x - 2)

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The equation -2/3x + y = -2 is in the slope-intercept form, which is a common form for linear equations.

What is the slope of the equation?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

we can use the two-point form to find the equation of the line:

y - y1 = m(x - x1)

Substituting the coordinates of the given point and the slope, we get:

y - (-2) = (-2/3)(x - 9)

Combining like terms and multiplying through the parentheses, we get:

y + 2 = -2/3x + 6

This equation is already in the form Ax + By = C, so we can simply use it as is:

-2/3x + y + 2 = 0

This equation can also be written as -2x + 3y = -6 by multiplying all the terms by 3 to get rid of the fraction.

The equation -2/3x + y = -2 is in the slope-intercept form, which is a common form for linear equations. In this form, the coefficient of x (-2/3) is the slope of the line, and the constant term (-2) is the y-intercept, which is the point where the line intersects the y-axis.

Hence, The equation -2/3x + y = -2 is in the slope-intercept form, which is a common form for linear equations.

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The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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Answer:The answer is D

Step-by-step explanation:

I know this because all the area of each face is equal to 10+10+52+32+40 and that is equal to 144in. squared

Answer:

D :)

Step-by-step explanation:

wait, have you smiled today? its very important:)

Answer:

43.75 ft²

Step-by-step explanation:

\(s_l\) = (l√(w/2)² + h²) + (w√(l/2)² + h²)

l & w become 3.5, and h becomes 6.

\(s_l\) = (3.5√(3.5/2)² + 6²) + (3.5√(3.5/2)² + 6²)

Step 1:Because this is a square pyramid, what you see above essentially becomes what you see below.

\(s_l\) = 2(3.5√(3.5/2)² + 6²)

Step 2: Divide 3.5 by 2 to get 1.75.

\(s_l\) = 2(3.5√1.75² + 6²)

Step 3: Square both 1.75 and 6 to get 3.0625 and 36 respectively.

\(s_l\) = 2(3.5√3.0625 + 36)

Step 4: Add 3.0625 and 36 to get 39.0625.

\(s_l\) = 2(3.5√39.0625)

Step 5: The square root of 39.0625 is 6.25.

\(s_l\) = 2(3.5 * 6.25)

Step 6: Multiply 3.5 by 6.25 to get 21.875.

\(s_l\) = 2(21.875)

Step 7: Multiply 2 by 21.875 to get 43.75.

\(s_l\) = 43.75 ft²

The lateral area of this pyramid is 43.75 ft².

Step-by-step explanation:

This is a geometric series, where the first term is -5 and the common ratio is -⅔.

aₙ = -5 (-⅔)ⁿ⁻¹

Refer to the attachment

Answer: slope: -9/2 y intercept: 75

Step-by-step explanation: I took the k12 test :)

Answer:

24

Step-by-step explanation:

If we have two square roots like \(\sqrt{36}\cdot\sqrt{16}\), we could do this either of two ways.

1. Multiply 36 by 16 and find the square root of that

\(\sqrt{36\cdot16} = \sqrt{576} = 24\)

2. Find the square root of both of them then multiply.

\(\sqrt{36} = 6, \sqrt{16} = 4, 6\cdot4 = 24\)

Hope this helped!

The triangle with side lengths √35 , √14 , 7 is a right triangle.

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

p² + b² = h² ( In a right-angled triangle)

p = perpendicular of the triangle

b = base of the triangle

h = hypotenuse of the triangle

According to the Pythagoras theorem:

p² + b² = h² (In a right-angled triangle)

In Option D

(√35)² + (√14)² = 7²

49 = 49

Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.

Hence, The triangle with side lengths √35, √14, 7 is a right triangle.

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The sequence of transformation that produce similar image is (d) a dilation followed by a rotation

Transformation involves changing the position and/or size of a figure.

There are four types of transformation, and they are:

The representation of the types of transformation are:

A dilation transformation would produce a similar image, while other transformation types would produce a congruent image

Hence, the sequence of transformation is (d)

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In order to simplify this expression, we need to use the following property:

So we have:

Therefore the answer is 26^9.

Answer:

26^9

Step-by-step explanation:

i just got the question right

Answer:

First, we need to calculate the total amount of the pension for the first offer:

$58,000 x 0.016 x 20 = $18,560 per year

Then, we can calculate the monthly pension payment:

$18,560 / 12 = $1,546.67 per month

For the second offer, we need to calculate the annual pension amount:

$64,900 x 0.013 x 20 = $16,828 per year

And then the monthly pension payment:

$16,828 / 12 = $1,402.33 per month

Finally, we can calculate the difference in monthly pension payments:

$1,546.67 - $1,402.33 = $144.34

Therefore, the difference in monthly pension payments is $144.34.

It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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