For each value below, enter the number correct to four decimal places.

Answer: a unit rate is how much would you pay for one item  and a rate is a fixed price for a good or service

Step-by-step explanation:

Answer:

90 pretzel sticks.

Step-by-step explanation:

Answer:

Denzel had 90 pretzel sticks before he gave any away.

Step-by-step explanation:

1) He gives away 2/9 to Jane (He's got 7/9 pretzel sticks left after Jane).

2) The remaining pretzel sticks are broken into 6 portions. He gives away 1/6 to Hannah. Now he's got 5/6 pretzel sticks remaining. We are told that these 5 parts are worth 55 pretzel sticks.

3) 55 pretzel sticks divided into 5 equal parts is 11 pretzel sticks in each.

4) 2/9 + 1/6 pretzel sticks given away needs common denominators to add

4/18 +3/8 = 7/18 pretzel sticks given away in total

That means 11/18 pretzel sticks remained that he did not give away.  We are told the 11/18 represents his remaining 55 pretzel sticks.

5) Since we have now divided the whole lot of pretzel sticks into 18 pieces we have 7/18 given away plus 11/18 (55 remain), and we calculated each part is 5 pretzel sticks.

6) 5 x 18 parts = 90 pretzel sticks to begin with.

Answer:

-8.66666666666666666666666666666666666

-9

Step-by-step explanation:

Answer:

The correct answer is: u = 10,500. When the value of the alternative hypothesis is greater than that of the null hypothesis, the power of the test will be increased, so a value of u = 10,500 would yield the greatest power to reject the null hypothesis.

Answer:

-7/8

Step-by-step explanation:

rate of change is the same as slope so -7/8

Answer:

Step-by-step explanation:

find the rate of change from the equation:

y = -7/8x + 3

use the formula: y = mx + b

where:

y = how far up the line goes

m = slope

x = how far along

b = Y-intercept

so the rate of change is the same as the slope

therefore, the slope = -7/8

Answer:

greater than or equal

Step-by-step explanation:

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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Answer: 10

Step-by-step explanation:

Answer:

It is 10

Step by step:

20

- 10

__

10

Answer:

2) the graph has a positive slope. the slope is 15. the y-intercept is 50.

3) (4,110)

Answer:  -2.7h−1.3j+2

Step-by-step explanation:

you just do 6-4 since those are like terms

Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

Answer:

1

Step-by-step explanation:

The value of x is; x = 3.14

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

cos θ = base / hypotenuse

here, we get,

cos 17 = 3/x

so, we have,

0.956 = 3/x

so, x = 3.14

Hence, The value of x is;x = 3.14

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n can take values greater than 5 and less than 2.

The graph of 2n - 2 > 8 or n - 1 < 1 is

 (---------n values--------------)                                  (-----n values-------------)

<∞----(-9)-(-8)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8-9-------------------∞>

It is a statement of an order relationship between two numbers or algebraic expressions.

- greater than

- greater than or equal to

- less than

- less than or equal to

We have,

2n - 2 > 8 and n - 1 < 1

We need to find the value of n.

2n - 2 > 8

Adding 2 on both sides.

2n - 2 + 2 > 8 + 2

2n > 10

Divide both sides by 2

n > 5

Now,

n - 1 < 1

Add 1 on both sides

n - 1 + 1 < 1 + 1

n < 2

Thus,

n can take values greater than 5 and less than 2.

The graph of 2n - 2 > 8 or n - 1 < 1 is

 (---------n values--------------)                                  (-----n values-------------)

<∞----(-9)-(-8)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8-9-------------------∞>

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The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer:

2

Step-by-step explanation:

18+16+4=36

40-38=2

Answer:

2 cupcakes left

Step-by-step explanation:

40 - (18 + 16 + 1 + 1 + 1 + 1) = 2

The missing values are

<UTQ = 41 degree

x= 1

<UQT = 47 degree

We have a parallelogram QRST.

We know that the opposite sides of the parallelogram is equal and parallel then

QR || ST

QT || SR

Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)

<UTQ = 41

Similarly, <UQT = <SRQ = 47

Now, RU = UT

2x + 1= 3

2x = 2

x= 1

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Answer:

answer is -1 answer solution

The number of red counters in the bag is given as follows:

8.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.

The probabilities for this problem are given as follows:

The sum of the probabilities is of one, hence the value of x is obtained as follows:

2x + x + 0.45 + 0.25 = 1

3x = 0.3

x = 0.1.

Hence the proportion of red is given as follows:

0.2.

There are 18 blue counters in the bag, which is of 0.45 of the total amount, hence the total amount is obtained as follows:

0.45n = 18

n = 18/0.45

n = 40.

Meaning that the number of red counters is given as follows:

0.2 x 40 = 8.

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Answer:

3y

Step-by-step explanation:

Answer:

y intercept is 4

the equation is y= 3/4 + 4

Slope intercept equation y=mx+b

ATQ,

cost of a rose⇢r

cost of a daisy⇢d

cost of a bundle of green filler ⇢f

so ,

the expression that represents the cost of making 75 bouquets would be↷

75(5r) + 75(3d) + 75(4f)

or

75(5r+3d+4f)

hence,

option 3rd & 4th are correct✓

Answer:

The correct options are

=> (5r + 3d + 4f) + 75

=> 75(5r) + 75(3d) + 75(4f)

Step-by-step explanation:

Given:

There are uses 5 roses, 3 daisies, and 4 bundles of green filler to make one bouquet.

Cost of rose = r

Cost of Daisy = d

Cost of a bundle of green filler = f

The expression represents the cost for making 75 bouquets that would be,

=> (5r + 3d + 4f) + 75

OR

=> 75(5r) + 75(3d) + 75(4f)

Answer:

x+7 ≤ 20

Just take it step by step:

seven more than a number is a number plus 7 (x+7)- keep in mind we dont know what the number is so we use x to represent the number.

it then says it's equal to at most 20.

This means that it cant equal anything above 20 since 20 is the max. Therefore, it must be 20 and below that x+7 equals

x+7≤ 20

≤ -this symbol means less than or equal to

Step-by-step explanation:

The two angles are related in that they are supplementary angles

Supplementary angles would add tuo to 180 degrees according to the angle Theorem.

Adding the two given angles :

These angles are supplementary

The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.

Hence, the angles are related as they are supplementary angles .

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Answer:

\(144\pi\)

Step-by-step explanation:

\(\pi(r^{2} )\)

\(\pi(12^{2} )\)

\(144\pi\)

The spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.

An average is a single number taken as representative of a list of numbers, generally the sum of the numbers divided by how many numbers are in the list (the arithmetic mean).

The formula to calculate the average of given numbers is equal to the sum of all the values divided by the total number of values. Average = Sum of Values / Number of Values.

So, in this case:

Values: 25, 50, 75

Number of Values: 3

Thus, the average:

Sum of Values / Number of Values = (25 + 50 + 75) / 3 = 50

Hence, the spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.

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Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.​

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

\(Hypotenuse^2=Base^2+Perpendicular^2\)

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

\((9.85)^2=x^2+(x+5)^2\)

\(97.0225=x^2+x^2+10x+25\)

\(0=2x^2+10x+25-97.0225\)

\(0=2x^2+10x-72.0225\)

Here, \(a=2, b=10,c=-72.0225\). Using the quadratic formula, we get

\(x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\)

\(x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}\)

\(x=\dfrac{-10\pm \sqrt{676.18}}{4}\)

Approximating the value, we get

\(x=\dfrac{-10\pm 26}{4}\)

\(x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}\)

\(x=\dfrac{16}{4},\dfrac{-36}{4}\)

\(x=4,-9\)

Distance cannot be negative so \(x\neq -9.\)

Now we have \(x=4\)

\(x+5=4+5\)

\(x+5=9\)

Therefore, the base is 4 m and the height is 9 m.

The base, height to the top of the ladder and height of the ladder when connected together we will get a triangle and then apply Pythagoras theorem we get base 4.0 m and height 9 m.

According to this theorem, the hypotenuse l,  base b and opposite side a are connected by the equation written as follows:

hypotenuse² = base² + opposite side²

l² = a² + b².

Thus if we know either two sides or the triangle we can calculate the length of the unknown side of the triangle. It is given that the length of ladder is 9.85 m. It is placed against a wall and the base that is distance between foot and wall is 5 m less than the height to the top.

Assuming a triangle connecting these three points, the hypotenuse is the length of the ladder 9.85 m and let x be the base and opposite side that is the height to the top be x + 5. Now apply Pythagoras theorem.

9.85² = (x+5)² + x²

97.02 = 2 x² + 10x + 25

2 x² + 10x -72.02 = 0

Now solve for x using quadratic equation we get x = 4.00. The base of the triangle is 4 m and opposite side that is the height = x +5 = 4 +5 = 9m.

Therefore, base is 4 m and height to the top of the ladder is 9 m.

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Answer: The probability that both events A and B will occur is 5/18 or 0.28.

Step-by-step explanation:

To determine the probability that both events A and B will occur, we need to calculate the probabilities of each event separately and then multiply them together.

Event A: The probability of rolling a 5 or 6 on the first die is 2 out of 6 (since there are two favorable outcomes out of six possible outcomes on a fair six-sided die). Therefore, the probability of event A is 2/6 or 1/3.

Event B: The probability of not rolling a 1 on the second die is 5 out of 6 (since there are five favorable outcomes out of six possible outcomes). Therefore, the probability of event B is 5/6.

To find the probability that both events A and B occur, we multiply the probabilities:

Probability(A and B) = Probability(A) * Probability(B) = (1/3) * (5/6) = 5/18.

Step-by-step explanation: Notice that the angle diagonal

of the 114° is a vertical angle and vertical <'s are ≅.

Now, notice that we have two parallel lines cut by a transversal.

If two parallel lines are cut by a transversal, then

consecutive interior angles are supplementary.

So we can setup the equation 114 + y + 12 = 180.

Simplifying on the left gives us 126 + y = 180.

Now subtract 126 from both sides to get y = 54.

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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