Madelyn launches a toy rocket from a platform. The height of the rocket in
feet is given by h(t) = -16t² + 16t+ 96 where t represents the time in
seconds after launch. What is the appropriate domain for this situation?
Answer:

The solution of compound inequalities is -6 < x < 24.

A compound inequality is a sentence that contains two inequality statements connected by the words "or" or "and." The conjunction "and" denotes that both statements of the compound sentence are true at the same time. It is the intersection or overlap of the solution sets for the individual statements. "Or" indicates that the entire compound sentence is true if either statement is true. It is the union or combination of the solution sets for each individual statement. A conjunction is a compound inequality that contains the word "and."

Inequalities are expressions that do not have an equal sign between them.

Given,

X - 7<17or-6x>36

First,

x - 7 < 17

x < 17 + 7

x < 24

Similarly,

-6x >36

x < [tex]\frac{-36}{6}[/tex]

x < -6

Thus,  compound inequality's solution is -6 < x < 24

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It takes Bob 125.0633 seconds to cover the entire track.

Let the time taken by Bob to cover the track be x sec

Let the distance of the track be y m

Akira covers the whole track in 95 seconds

hence, his speed is y/95 m/s

Similarly, Bob's speed is y/x m/s

He has traveled to the Easternmost point in 22 seconds. Hence to meet Akira, he has to run for 4 more seconds.

In that time he will cover a distance of 4y/95 m

Similarly, in 26 seconds, Bob will cover

26 y/x m/s

Now Akira has started from the Northernmost point, and we all know that the distance between the Easternmost and Northernmost points of the track will be 1/4th of the whole track length.

Hence,

4y/95 + 26y/x = y/4

or, y(4/95 + 26/x) = y/4

or, 4/95 + 26/x = 1/4

or, (4x + 2470)/95x = 1/4

or, 4x + 2470 = 95x/4

or, 16x + 9880 = 95x

or, 79x = 9880

or, x = 125.0633 seconds

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Answer:

A) -20

Step-by-step explanation:

[tex]4y(4y-4)-4(-4y+5+4y^2)\\\\16y^2-16y + 16y-20-16y^2\\\\-20\\[/tex]

Using ratio and proportions, Jacob has mixture with stronger basil taste

Ratio can be defined as a comparison between two or more numbers that shows their sizes in relation to each other. A ratio often compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Proportion can be defined as equality of two ratios. Two equivalent ratios are always in proportion. Proportion is an equation or statement that shows that the two ratios or fractions are equivalent.

In this case, we can compare the ratio and determine which will have a stronger basil taste.

Lupita mixed 2 tsp of basil for 3tsp of oregano

The ratio of basil to oregano = 2/3 = 0.67

Jacob mixed 4 tsp of basil for 5 tsp of oregano

The ratio of basil to oregano = 4/5 = 0.8

Comparing the ratios, Jacob ratio is higher compared to Lupita and makes Jacob have the strong basil taste.

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We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.

A sample space can be defined as the set of all possible outcomes of any experiment.

We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅}  (i)

This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)

Using the values of (i) and (ii), we get -

= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.

= p|C|=|A||B|.

From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|.  if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.

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The annual growth rate is 4.73 %

The continuous growth rate is 4.62 %

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

Let us assume:

The initial amount of 1, so results are 2.

Let x be the  percent in decimal form

Growth rate per year:

[tex]1(1+x)^{15} = 2[/tex]

Take ln on both the sides

[tex]ln((1+x)^{15}) = ln(2)[/tex]

15*ln(1+x) =0 .693

ln(x+1) = 0.693/15

ln(x+1) = 0.04621

Take anti ln on both the sides

x+1 = 1.0473

x = 1.0473 - 1

x = .0473

x =4.73 % annual growth rate

Continuous growth rate:

[tex]1*e^{15x} = 2[/tex]

[tex]ln(e^{15x}) = ln(2)[/tex]

15x*ln(e) = ln(2)

ln(e) = 1

15x =0.693

x =0 .693/15

x = .0462

x = 4.62 %

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One pipe takes 6 hours to fill the pool and the other takes 12 hours.

Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.

Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:

4(1/x + 1/y) = 1

You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.

So, Pipe A, working for t hours, fills half the pool:

t(1/x) = 1/2

And Pipe B, working for 9 - t hours, fills half the pool:

(9-t)(1/y) = 1/2

You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):

4(1/x + 1/y) = 1

t(1/x) = 1/2

(9-t)(1/y) = 1/2

Solve for t in that second equation, then plug it into the third equation:

t(1/x) = 1/2

t = x(1/2)

t = x/2

(9 - x/2)(1/y) = 1/2

Now you've got a system of two equations:

4(1/x + 1/y) = 1

(9 - x/2)(1/y) = 1/2

Solve for y in the second equation, then plug that into the first equation:

(9 - x/2)(1/y) = 1/2

(9 - x/2) = y(1/2)

2(9 - x/2) = y

18 - x = y   (this is a really nice-looking form of that equation; we'll use it again later)

4(1/x + 1/y) = 1

4(1/x + 1/(18-x)) = 1

4/x + 4/(18-x) = 1

(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1

(4(18-x) + 4x)/(x(18-x)) = 1

4(18-x) + 4x = x(18-x)

72 - 4x + 4x = 18x - x2

72 = 18x - x2

x2 - 18x + 72 = 0

(x - 6)(x - 12) = 0

x - 6 = 0    OR    x - 12 = 0

x = 6  OR    x = 12

So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.

When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.

These cases are equivalent, since the original problem makes no distinction between the pipes.

Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.

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Answer:

1/8(3x+4y+3)

Step-by-step explanation:

Answer:

1) slope = 1/2 2) slope= -1 3)slope= 1/2 4) 5/4

Step-by-step explanation:

if you want y intercpt form

1) y=1/2x

2)y= -x-3

3) y= 1/2x-3.5

4) y= 5/4x - 1

The required hypothesis for the given data of the problem is  

Null hypothesis H₀: μ=$1200 , n = 35

Alternate hypothesis Hₐ : μ > 145

In statistics, a two-followed test is a technique wherein the basic region of a dissemination is two-sided and tests whether an example is more noteworthy or under a scope of values. It is utilized in invalid speculation endlessly testing for measurable importance.

We have,

the board members insist that the parking garage cannot be funded by raising property taxes, the mean daily parking revenue collected must be greater than $1,200

So, Null hypothesis H₀: μ=$1200 , n = 35

Then, Alternate hypothesis Hₐ : μ > 145

Standard deviation = $196

Thus, It is right tailed hypothesis.

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The change in her investment, due to the lost money is $112

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

Rate of loss = $4 per day

Duration = 4 weeks

From the above parameter, we can calculate the amount of money lost to the investment using:

Amount lost = Duration * Rate of loss

Substitute the known values in the above equation

So, we have the following equation

Amount = 4 weeks * $4

Convert weeks to days

Amount = 28 * $4

Evaluate the quotient

Amount = $112

Hence, the amount is $112

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It is more unusual to have a high temperature of 55 degrees in July because the month's z-score is 2.375 standard deviations from its mean.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. Standard deviation is significant because it enables consumers to evaluate risk. Think about an investing strategy with a 10% average yearly return.

Here,

Calculations are attached in image.

A high temperature of 55 degrees is particularly rare since July's z-score is 2.375 standard deviations outside of its mean.

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Answer:

24

Step-by-step explanation:

the answer is 24 because 3 gallons can definitely do more then 16 it also depends on how much water the cups can hold.

Answer: I think the answer is 2

Step-by-step explanation:

The smaller of the two shapes is 12, and the larger of the two shapes is 16,

I found that the difference between the two is 4 (or 16 - 12 =4). If x = 6 and the difference is 4, then subtract 4 from 6 and the answer will come out to be 2

16-12=6-4

y=2

Answer: T-62

Step-by-step explanation: i think this is correct

The solution is, the value we get, t = 62.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

8(t+2) -3(t-4)=6(t-7)+8

or, 8t + 16 -3t +12 = 6t - 42 +8

or, 5t + 28 = 6t - 34

or, t = 62

Hence, The solution is, the value we get, t = 62.

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Answer:

The number of peaches and the number of mangos that Savannah bought

are 4 and 10 respectively.

The variable use to write the equation is x and it is the number of peaches

Savannah and her children bought

let

the number of peaches Savannah and her children bought = x

Therefore

the number of mangoes Savannah and her children bought = x + 6

The total worth of what they bought = $22

Therefore,

1.75x + 1.50(x + 6) = 22

1.75x + 1.50x + 9 = 22

3.25x + 9 = 22

3.25x = 22 - 9

3.25x = 13

x = 13 / 3.25

x = 4

Therefore,

number of peaches bought = 4

number of mangoes bought = 4 + 6 = 10

Step-by-step explanation:

Answer: 6 Peaches and 2 Mangos

Step-by-step explanation: If one peach is worth $1 and one mango is worth $2, to get $10 used you need to buy 6 peaches and 2 mangos since 2 + 2 = 4 and 6 + 4 = 10

Answer: Store B and C sell at a lower unit price.

Step-by-step explanation:

Store B: $3.48/3 = $1.16 per pound.

Store C: $3.80/4 = $0.95 per pound.

Answer:

30

Step-by-step explanation:

Triangles add up to 180.

Your known sides are: 15x, 31x-2, and 90 (the square on the corner of the angle tells you that it's a right angle or 90 degrees.)

First make an equation to find X

this looks like: 15x+31x-2+90=180

I just added the sides we know and set them to equal 180. Because triangles add up to 180.

Now solve this by first combining like terms

15x+31x-2+90=180 (do the numbers with x's) so 15x+31x

46x-2+90=180 (now combine the numbers without X's) so -2+90

46x+88=180 (now since 88 is positive, do the opposite and subtract it from 180. This is because 180 is on the other side of the = sign.)

46x=92 (now since 46x means 46 times x, you do the opposite of multiplication and divide 92 by 46.

This gives you x=2

Now the last thing you need to do is solve for angle A

Angle A says "15x" so you can substitute our x value (2) for the x

This looks like 15(2)    15 times 2 is 30

so 30 should be your answer

Using the compound interest formula, we know that $7,672 is the interest on investments earned.

The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.

The resulting value is subsequently deducted from the loan's entire original amount.

So, interest earned on investment:

A = 9,875 (1 + 0.048/12)^ 12(12)

A = $ 15,547

Interest on investments is the money received:

= $ 15,547 - $ 9,875

= $ 7,672

Therefore, using the compound interest formula, we know that $7,672 is the interest on investments earned.

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Complete question:

An investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much interest is earned on the investment?

a. $4,740

b. $7,458

c. $7,672

d. $17,567

Answer:

PAy Attention Triangle

Step-by-step explanation:

Triangle ABC is isolated True

The answer is $12.50

You can see on the graph that if the weight is 20 pounds, it will cost $10. We are looking for how much it will cost to ship a 25 pound package. It can’t be $20.00 either.

hope this helps!

Give me Brainliest please!

This study can be best described as Controlled Placebo Experiment

What is a Controlled Placebo Experiment?

A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.

According to the given question:

This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.

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The hypotenuse - leg congruency can be applied in both right triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

In other words, if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

Hence, the legs of the right triangle are congruent and one of the legs are congruent.

Therefore, the hypotenuse - leg congruency can be applied.

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The Residual is defined as the difference between the actual and predicted, or fitted values of the response variable. This statement is true.

Linear regression is a statistical tool that determines how well a straight line fits a set of paired data. The straight line that best fits that data is called the least squares regression line. This line can be used in a number of ways. One of these uses is to estimate the value of a response variable for a given value of an explanatory variable. Related to this idea is that of a residual.

Residuals are obtained by performing subtraction. All that we must do is to subtract the predicted value of y from the observed value of y for a particular x. The result is called a residual.

The formula for residuals is straightforward:

Residual = observed y – predicted y

It is important to note that the predicted value comes from our regression line. The observed value comes from our data set.

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The expression that represents the orders is 12 * (5 + 3.5)

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

The above parameters mean that:

Expression for Sean's purchase = Number of cupcakes in a box * (Number of boxes ordered for his sister’s graduation party + Number of boxes ordered for the Variety Show party)

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

Expression for Sean's purchase = 12 * (5 + 3.5)

Hence, the expression is 12 * (5 + 3.5)

In (a), we have

Expression = 12 * (5 + 3.5)

Evaluate the sum

Expression = 12 * 8.5

Evaluate

Expression = 102

This means that the total number of box is 102

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Complete question

A baker packages 12 cupcakes to a box. Sean orders 5 boxes for his sister’s graduation party and 3.5 boxes for the Variety Show party. Write an expression that shows the calculations you could use to find the number of cupcakes Sean orders.

Write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have

One possible volume of a graduated cylinder produced by the company is 98 cubic inch.

The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object. An object with a larger volume would occupy more space.

The volume of a cube can be found by multiplying the edge length three times. For instance, if the length of an edge of a cube is 4, the volume will be 4³. The formula to calculate the volume of a cube is given as,

Volume of a cube = s³, where 's' is the length of the side of the cube.

Given in the question:

Radius of cylinder = 2 inches.

Height of the cylinder = 7.75 to 8 inches.

We know that,

Volume of Cylinder = πr²

For minimum Volume 7.75 :

                   Volume = πr²× 7.75

                                 = 3.14 × 4 × 7.75

                                 = 97.34 cubic inches.

For maximum volume 8.00 inches

                       Volume = πr² × 8

                                     = 3.14 × 4 × 8

                                     =  100.81

Therefore, the possible volume could be between 97.34 cubic inches and 100.81 cubic inches.

Thus, the volume is 98 cubic inches.

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The confidence interval is (0.309, 0.389).

Calculate a 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.

Sample size, n = 782

Sample proportion, p = x/n = 0.349105

Confidence level, 1 - α = 98% = 0.98 Implies

Level of significance, α = 0.02

At α = 0.02, the two-tailed critical value from the z-table, Zα/2 = 2.33

Then, the 98% confidence interval is,

It gives, 0.309≤ p ≤0.389

Lower endpoint = 0.309

Upper endpoint = 0.389

We are 98% confident that the proportion of all suspected criminals who were captured is within the confidence interval. If we were to take a large number of random samples of size 782, 98% of the resulting confidence intervals would contain the true proportion of all suspected criminals who were captured.

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The times that buses arrive at bus stops in various cities and in various climates are noted by a researcher in a notebook. This study is an observational one. Here option D is the correct answer.

It is an observation because it involves systematically noting people's actions, things, and occurrences without engaging in conversation or other interactions. In observational studies, the impact of a risk factor, diagnostic test, therapy, or other intervention is observed without an attempt to alter who is or is not exposed to it.

Two categories of observational studies are cohort studies and case-control studies. It cannot be a single-blind experiment, nor can it be a double-blind experiment since it is not an experiment.

Single-blind refers to a subject or an assessor. When a study is double-blind, neither the patient nor the outcome evaluator is aware of who received the prescription. It is not a survey because it relies on interviews with a representative sample of people as the main way of gathering data.

Complete question:

A researcher writes down in a notebook the arrival times of different city buses at a bus stop during different weather conditions. Which kind of study is this?

A - observational

B - survey

C - single-blind experiment

D - double-blind experiment

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