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The solution of the expression at x = 2 is 53 and at x = 7 is 33.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is h(x) = −4x + 61. The value of the expression at x = 2 and x = -7 will be calculated as:-

At x = 2,

h(x) = −4x + 61

h(2) = -4 x 2 + 61

h(2) = -8 + 61

h(2) = 53

At x =7

h(x) = −4x + 61

h(2) = -4 x 7 + 61

h(2) = -28 + 61

h(2) = 33

Therefore, the values are 53 and 33.

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To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.

Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.

Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.

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The rounding off the value 0.1347 to the nearest tenth is 0.1

What is rounding off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.

Given, 0.1347 round to the nearest tenth

While rounding to the nearest tenth, the value after the digit has been noticed.

In the number 0.1347, rounding to the nearest tenth, digit 3 should play a role to round the digit 1 which is in the tenth position. 3 is not equal to 5 and less than 5.

So, 0.1347 becomes 0.1

Hence, the required answer is 0.1

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Answer:

4a + b - $1.40 = 2b

Step-by-step explanation:

Different style of problem here, so here's my guess

Let...

A = Tshirts

B = Sweaters

4a + b - $1.40 = 2b

4a + b indicates 4 shirts plus 1 sweater

The -$1.40 at the end indicates $1.40 less than

=2b indicates 2 sweaters

mZDAE is a line segment that connects the midpoints of line segments BA and CE. In the diagram, its coordinates are (66⁰, 52%).

The probability that at least one of the disks selected has a number greater than 24 is 127/343.

To find the probability that at least one of the disks selected has a number greater than 24, we can find the probability that all three disks have numbers less than or equal to 24 and subtract this from 1.

The probability that a disk selected from a container has a number less than or equal to 24

24/28= 6/7

Since,

there are 24 disks with numbers less than or equal to 24 out of a total of 28 disks in each container.

We can assume that the selection of a disk from one container is independent of the selection of a disk from another container, so the probability that all three disks selected have numbers less than or equal to 24 is (6/7)³

since we are making three independent selections.

Therefore,

The probability that at least one of the selected disks has a number greater than 24 is 1 - (6/7)³ ,

which simplifies to 343/343 - 216/343 = 127/343

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Note that the body starts "with an initial velocity and moves with uniform acceleration."(Option C)

In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.

The distance covered by the particle in nth second

Sₙ = u + a/2(2n-1)

S₈ = 20m

S₈ = u + a/2(2x(8-1)

20 = u + 7.5a ...................()

S₉ = 22 = u + a/2(2*9-1)

22 = u + 8.5a ..................(2)

By solving equations 1 and 2 we have :

u=5m/s , a=2m/s²

Thus,

S₁₀ = u+ a/2(2*10-1)

S₁₀ = 5 + 1/2 * 2 (2 * 10-1)

S₁₀ = 5 + 19

S₁₀ = 24m

Thus, it is correct to state that the body starts with the initial velocity and moves with uniform acceleration, and the correct option is C.

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Full Question:

A body covers 20 m, 22 m, 24 m, in 8th, 9th, and 10th seconds respectively. The body starts:

from rest and moves with uniform velocity.

from rest and moves with uniform acceleration.

with an initial velocity and moves with uniform acceleration.

with an initial velocity and moves with uniform velocity.

Answer:

D

Step-by-step explanation:

The 6 represents the initial value of 6000.  The cases are going down 5,000 a month.

Answer:

Step-by-step explanation:

Sorry cant help 18.85%

They will be 74 km apart after 2 hours.

What is the relative speed of two moving objects?

For two objects, the relative speed between them equals the change in distance between them divided by the change in time. If two bodies are going in opposite directions, their relative speed is equal to the sum of their individual speeds. If they are moving in the same direction, their relative speed is equal to the difference in their individual speeds.

Given here,  the Serenity travels at 17 mph and the Mystic travels at 20 mph  in the opposite direction .

therefore,  the relative speed is sum of their speeds = 17 + 20 = 37 mph

After 2 hours the distance between them would be = 37 × 2 = 74 mph

Hence, they  will be 74 km apart after 2 hours.

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Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.

What is overtime pay?

Overtime pay is the additional compensation paid to an employee for any hours worked in excess of the standard working hours or beyond the standard workweek. The rate of overtime pay is usually higher than the regular rate of pay for an employee's normal working hours.

To determine the extra overtime pay due to Casey Na for the first quarter, we need to know his regular pay rate and the number of hours he worked each week.

Let's assume that Casey Na's regular pay rate is $20 per hour and that he worked 40 hours each week during the first quarter. This means that he worked 3 hours of overtime each week, for a total of 39 hours at his regular rate and 3 hours at his overtime rate.

To calculate his overtime pay for the first quarter, we can use the following formula:

Overtime pay = overtime hours x overtime rate

Since Casey Na worked 3 hours of overtime each week for 13 weeks, his total overtime hours for the first quarter were:

Total overtime hours = 3 hours/week x 13 weeks = 39 hours

His overtime rate is 1.5 times his regular rate, or $20 x 1.5 = $30 per hour.

Therefore, his overtime pay for the first quarter was:

Overtime pay = 39 hours x $30/hour = $1,170

Since he also earned a bonus of $975 for perfect attendance, his total extra pay for the first quarter was:

Extra pay = Overtime pay + Bonus = $1,170 + $975 = $2,145

Therefore, Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.

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Solution of the system of equations y - x²- 14x = 54 and 43 = y - 6x are

x = -4 ± √5 and y = ± 6√5 + 19

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given equations

y - x²- 14x = 54

y = x² + 14x + 54            -------------(1)

43 = y - 6x

y = 6x + 43                     ------------(2)

By equation (1) and (2)

6x + 43 = x² + 14x + 54

x² + 14x + 54 - 6x -43 = 0

x² + 8x + 11 = 0

a = 1, b = 8, c = 11

x = (-b ± √(b² - 4ac))/2a

x  = (-8 ± √(64 - 4.11))/2

x  = -4 ± √16-11

x = -4 ± √5

Putting value of x in equation (2)

y = 6(-4 ± √5) + 43

y = -24 ± 6√5 + 43

y = ± 6√5 + 19

Hence, x = -4 ± √5 and y = ± 6√5 + 19 are the solutions of equations

y - x²- 14x = 54 and 43 = y - 6x.

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The ways the system of equations 9x - 2y = 43x+8y=12can be solved are:

A) Multiply the first equation by 4, then add the equations.

D) Multiply the second equation by 3, then subtract the equations.

From the given equations,9x - 2y = 43x+8y=12we need to use wyas of solving simultaneous equation to solve it.

Then if we Multiply the first equation by 4,  thge we can then perform addition to the second equation like

9x - 2y = 4

36x - 8y = 4

3x+8y=12

then if we add to equation 2 we have

39x =12

then we can solve x = 12/39

The same can be done with equation D .

Therefore, option A and D are correct.

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Answer:

Step-by-step explanation:

To solve the system of equations:

9x - 2y = 4 ...(1)

3x + 8y = 12 ...(2)

We can use elimination method by adding or subtracting the equations in a way that one variable is eliminated.

Here are the possible ways to solve the system:

A) Multiply the first equation by 4, then add the equations.

Multiplying the first equation by 4 gives:

36x - 8y = 16

Adding the resulting equation to the second equation gives:

36x - 8y + 3x + 8y = 16 + 12

Simplifying the equation:

39x = 28

x = 28/39

Substituting x in equation (1) gives:

9(28/39) - 2y = 4

Solving for y gives:

y = -155/78

Therefore, the solution is (x,y) = (28/39, -155/78).

B) Multiply the second equation by 3, then add the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Adding the resulting equation to the first equation gives:

9x - 2y + 9x + 24y = 4 + 36

Simplifying the equation:

18x + 22y = 40

Dividing the equation by 2 gives:

9x + 11y = 20

Substituting 9x from equation (2) gives:

3x + 8y = 12

Solving for x gives:

x = (12 - 8y)/3

Substituting x in equation (3) gives:

9[(12-8y)/3] + 11y = 20

Solving for y gives:

y = 16/39

Substituting y in equation (2) gives:

3x + 8(16/39) = 12

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

C) Multiply the first equation by 3, then add the equations.

Multiplying the first equation by 3 gives:

27x - 6y = 12

Adding the resulting equation to the second equation gives:

27x - 6y + 3x + 8y = 12 + 12

Simplifying the equation:

30x = 24

x = 4/5

Substituting x in equation (1) gives:

9(4/5) - 2y = 4

Solving for y gives:

y = -23/10

Therefore, the solution is (x,y) = (4/5, -23/10).

D) Multiply the second equation by 3, then subtract the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Subtracting the second equation from the first equation gives:

6x - 26y = -8

Solving for x gives:

x = (26y - 8)/6

Substituting x in equation (2) gives:

3[(26y-8)/6] + 8y = 12

Solving for y gives:

y = 16/39

Substituting y in equation (1) gives:

9x - 2(16/39) = 4

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

The solution to the statistics have been given below

The probability = 3 / 4 = 0.75

n = 933

x≥ 729

np = 0.75 * 933

= 699.75

√933 * 0.75 * 0.25

= √174.9375

= 13.23

using the continuity correction we have

729 - 0.5

= 728.5 -  699.75 /  13.23

= 2.17

The p value is 0.015003.

there is a 1.5% chance of getting  729 peas with red flowers

b. given that Z is greater than 2, this can be said to be high

c. These results suggest that the scientist maybe wrong in his assumption

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If the researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, then the researcher was using a stratified sampling method.

Here a researcher divided subjects into three groups according to whether or not they have brown, blue, or green eyes.

The selected members from each group for their sample

The stratified sampling method is defined as the sampling method that divides the total population into the smaller group

Here the total population is divided into three groups according to whether they have brown, blue or green eyes.

Therefore, researcher was using stratified sampling method

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Answer:

Step-by-step explanation:

Given the volume of a cylinder, V = πr^2h, where r is the radius, h is the height, and π is Pi, we can find the radius by rearranging the equation and solving for r.

V = πr^2h, so r^2 = V / (πh)

Taking the square root of both sides, we have:

r = √(V / (πh))

Substituting the given values:

r = √(950 / (π * 10))

Since Pi is approximately equal to 3.14, we can calculate the approximate value of r:

r = √(950 / (3.14 * 10))

r ≈ 7.46

Therefore, the radius of the cylinder with a volume of 950 cubic inches and a height of 10 inches is approximately 7.46 inches.

Answer:

6 units

Step-by-step explanation:

Since the two angles are equal, this means that the triangle is isosceles. So x+4 = 3x-8. After solving, 2x = 12,  x = 6. So AC is 6 units.

Answer: 6 units

Step-by-step explanation:

Since this is an isosceles triangle lines AB and BC are congruent so

x + 4 = 3x - 8 ---- add 8 and subtract x on both sides

12 = 2x ---- divide by 2 to isolate the x

x = 6

a. The amount of copper in a bronze of 360g is 324g

b. The mass of bronze with 670.5g of copper is 745g

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The ratio of copper to Tin is 9:1. The total ratio is 10

a.therefore the amount of copper = 9/10 × 360

= 324g

b. The mass of copper = 670.5g

therefore the mass of the bronze =

= 9/10× y = 670.5

9y = 670.5 × 10

9y = 6705

y = 6705/9

y = 745g

therefore the total mass of the bronze is 745g

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The graph that best models the exponential function is given as follows:

Graph A.

An exponential function is defined as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

y = 200000(1.06)^x.

The value of the home after 5 years is given as follows:

y = 200000(1.06)^5

y = $267,645.

Which is best approximated by the Graph A.

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The volume is 3315 cubic feet.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given polynomial function is V(x)=x³-4x.

Here, W(x)=V(3x)

Replace x by 3x in the function V(x)=x³-4x, we get

V(3x)=(3x)³-4(3x)

V(3x)=27x³-12x

W(x)=27x³-12x

Replace x by 5 in the function W(x)=27x³-12x, we get

Now, W(5)=27(5)³-12(5)

= 27×125-60

= 3375-60

= 3315 cubic feet

Hence, the volume is 3315 cubic feet.

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

A polynomial function V(x)=x³-4x that represents the volume of the right triangle pyramid when measured in cubic feet.

The function (x) =(3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards.

Find a function W(x) that gives us the volume when measured in yards also to find W(5).

The proper way to construct a stem-and-leaf plot to display the data set {62,67,68,73, 73, 79,91,94,95,97} is to include a stem labeled ‘8’ and enter no leaf on the stem. So, the correct choice is option (b).

A stem and leaf graph is like a special table where each data value is separated into a "stem" (the first number) and a "leaf" (usually the last number). Leaves are sorted in ascending order from left to right. We have a data set with values {62,67,68,73, 73, 79,91,94,95,97}. Now, to construct the stem- leaf plot for our data.

Stem | Leaf

6 | 2 7

7 | 3 3 9

9 | 1 4 5 7

For stem and leaf diagram if some values are not present for some stem, then no leaf should be added to that stem. If we skip that stem than it would distort the shape of distribution of the data.

stem | leaf

6 | 2 7

7 | 3 3 9

8 |

9 | 1 4 5 7

Hence, include a stem labeled 8 and enter no leaves on the stem.

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Complete question:

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a)exclude a stem labeled ‘8

b)include a stem labeled ‘8’ and enter no leaves on the stem.

c) include a stem labeled ‘(8)’ and enter no leaves on the stem.

d) include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem.

Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.

The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:

m = (4 - (-1)) / (4 - (-3)) = 5 / 7

So the slope of the line BC is 5/7.

One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:

b = y - mx

where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:

b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7

So the equation of line BC in the slope-intercept form is:

y = (5/7)x - 16/7

Step-by-step explanation:

These are the four points that are exactly 5 units away from point W. To find points that are 5 units from point W, which is located at (-5, -3).

To find points that are 5 units from point W, which is located at (-5, -3), we need to find all points that are a distance of 5 units away from (-5, -3) using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the distance between two points) is equal to the sum of the squares of the lengths of the other two sides

Given a point (x, y), the distance between that point and point W can be found using the formula:

distance = sqrt((x + 5)^2 + (y + 3)^2)

Setting this distance equal to 5 and solving for x and y, we get the following points:

(0, -8), (-10, -8), (0, 2), and (-10, 2).

These are the four points that are exactly 5 units away from point W.

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total cookies first to find ratio values

8 + 9 + 7 + 6 = 30 total

first ratio is sugar cookie to total

7 / 30 chances

after eating the sugar cookie, the total reduces to 29

second ratio is the new total

8 / 29 chances.

potential bonus??

the odds of this happening in this exact order is both odds multiplied.

so (7/30) × (6/29) = 7 / 145 chances she completes this in the exact order stated.

The answers to the geometry questions are given as follows:

2)

a)

A = 8

b = 10

x = 118°

y = 62°

b)

a = 8

b = 15

y = 50

x = 100°

3)

(a)

∠2 = 25°

3 = 65°

∠4 = 65°

∠5 = 90°

(b)

since SL = 10,

i) LT  10

ii) TM = 10

iii) SM = 10

4)

a) Since m∠118

∠2 = 18°

∠3 = 72°

∠4 = 72°

If FA = 27, then LO = 13.5

5)
a) All the angles in the diagram are equal to ∠45°
b) Line BC = 6√2
c) Line BE  = 6

The above are solved using the principles behind the properties of Parallelograms; Rhombus, Rectangle, and Square.

Since the above answers are justified by the qualities or properties of :

Parallelograms; Rhombus, and Rectangle, let's look at them one by one.

2

a)

A = 8 - opposite sides of a parallelogram are equal in length

b = 10 -opposite sides of a parallelogram are equal in length

y = 62° - opposite angles of a parallelogram are of equal measure.

x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2

= 118°

3)

(a) Here we have a Rhombus.

∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2

∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°

∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3

∠5 = 90° - [properties of a Rhombus]

(b)

since SL = 10,

i) LT  10 - All sides of a Rhombus are equal

ii) TM = 10 - All sides of a Rhombus are equal

iii) SM = 10 - All sides of a Rhombus are equal

4) Here we have a Rectangle.

a) Since m∠18

∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)

∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ =  90-18 = ∠72°

∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)

If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,

LO = FA/2

LO = 27/2

LO = 13.5

5) Here we have a square.
a) All the angles in the diagram are equal to ∠45°. This is because, the diagonals bisect all interior angles. Since each interior angle is 90°, thus, each of the resulting angle bisected 45°

b) Line BC = 6√2 - This is be
c) Line BE  = 6

The length of one-half of the diagonal of a square can be found using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

Let s be the side length of the square. Then, the length of the diagonal of the square (d) can be found using the equation d = s√2.

In this case, s = 6√2. So, the length of the diagonal (d) is:

d = s√2 = (6√2)√2 = 6(√2)(√2) = 6(2) = 12

Therefore, one-half of the diagonal of the square is:

(1/2)d = (1/2)(12) = 6

So, the length of one-half of the diagonal of the square ABCD is 6.

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you do not give the answer choice in this picture, but I assume it is along the lines of this

The scatter plot shows a negative association between variable X and Y