The number of question on a math test is represented (3x+1). The number of questions on the spelling test is represented by (x+12). Write an expression to find how many more questions were on the math test. Then evaluate the expression if the value x is 8

Answer:

The 4th graph

Step-by-step explanation:

To determine which graph corresponds to the  [tex]f(x) = \sqrt{x}[/tex]  we will start with inserting some values for x and see what y values we will obtain and then compare it with graphs.

[tex]f(1) = \sqrt{1} = 1\\f(2) = \sqrt{2} \approx 1.41\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]

So, we can see that the pairs (1, 1), (2, 1.41), (4, 2), (3, 9) correspond to the fourth graph.

Do not be confused with the third graph - you can see that on the third graph there are also negative y values, which cannot be the case with the [tex]f(x) =\sqrt{x}[/tex], the range of that function is  [tex][0, \infty>[/tex], so there are only positive y values for [tex]f(x) = \sqrt{x}[/tex]

Answer:

if your on edge its the last one

Step-by-step explanation:

use the graphing calculator and input the equation and it will be fourth graph

Answer:

33 hearts sold, 48 roses sold

Step-by-step explanation:

x- number of roses sold

y- number of hearts sold

x=15+y <- " The number of bouquets sold was 15 more than the number of hearts sold"

5x+3y=339

5(15+y)+3y=339

75+5y+3y=339

8y=339-75

8y=264

y=33

x=15+33=48

The number of chocolate hearts sold was 33, and the number of bouquets sold was 48 for a total revenue of $339.

Let's assume the number of chocolate hearts sold was 'x'. Since the number of bouquets sold was 15 more than the number of hearts sold, the number of bouquets sold would be 'x + 15'.

The price of each rose bouquet is $5, so the total revenue from selling bouquets would be '5(x + 15)'.

Similarly, the price of each chocolate heart is $3, so the total revenue from selling hearts would be '3x'.

Since the total revenue collected was $339, we can set up an equation: '5(x + 15) + 3x = 339'.

Simplifying the equation, we get '8x + 75 = 339'.

Subtracting 75 from both sides of the equation, we get '8x = 264'.

Dividing both sides of the equation by 8, we get 'x = 33'.

Therefore, 33 chocolate hearts were sold, and the number of bouquets sold would be '33 + 15 = 48'.

Answer:

Population : all the steaks Tessa can cook

Parameter : minimum internal temperature of 160 degrees Fahrenheit

Sample : two random thermometer readings

Statistic : minimum sample reading of 165 degrees Fahrenheit

Step-by-step explanation:

Let's recall the definitions of these statistical concepts and match it with the information that were provided to us:

The two numbers are 8,13.

Step-by-step explanation:

Let,

smaller number = x

Larger number = x+5

According to given statement;

Smaller number + Bigger number = 3x-3

[tex]x+(x+5)=3x-3\\x+x+5=3x-3\\2x+5+3=3x\\8 = 3x-2x\\8=x\\x=8[/tex]

Smaller number = 8

Larger number = 8+5 = 13

The two numbers are 8,13.

Keywords: algebraic equation, addition

Learn more about addition at:

#LearnwithBrainly

Answer:

The two numbers are 8,13.

Answer:

Ratio of the increase in value to the original value will be 1 : 5

Step-by-step explanation:

This question is incomplete; Here is the complete question.

A house with an original value to $150,000 increased in value to $180,000 in 5 years. what is the ratio of the increase in value to the original value of the house?

Original value of the house = $150000

Value of the house after 5 years = $180000

Appreciation in value of the house after 5 years = $180000 - $150000

= $30000

Now the ratio of the increase in value to the original value = [tex]\frac{\text{Increased value}}{\text{Original value}}[/tex]

= [tex]\frac{30000}{150000}[/tex]

= [tex]\frac{1}{5}[/tex] or 1 : 5

Therefore, ratio of the increase in value to the original value of the house is 1 : 5

Final answer:

To find the ratio of the increase in house value to the original value, subtract the original price from the increased price, then divide by the original price. For a house purchased at $200,000 and increased to $250,000, the ratio would be 0.25, or a 25% increase from the original value.

Explanation:

To calculate the ratio of the increase in value to the original value of a house, you must take the difference between the final value and the original value, then divide this by the original value. Suppose a house was bought for $200,000 and is now worth $250,000, this would be an increase of $250,000 - $200,000 = $50,000. The ratio of increase to original value would thus be $50,000 / $200,000 = 0.25 or 1:4. This indicates that, for every dollar of the original value, the house increased in value by 25 cents. If we wanted to express this as a percentage, we would multiply by 100, giving us a 25% increase in value. However, it's important to remember other factors such as transaction costs, market conditions, and loan repayment when considering the rate of return on a house.

Answer:

800 months

Step-by-step explanation:

The formula for interest is:

(Capital * saving account * time) / 100

So:

(10000 * 0.06 * x) / (100) = 4800

We clear x:

(10000 * 0.06 * x) = (100) * 4800

x = 480,000 / (10000 * 0.06)

x = 800 months (66.67 years)

To determine the duration for which the deposited $10,000 at 6% interest grew to a total of $14,800 ($10,000 principal + $4,800 interest), the formula for compound interest can be re-arranged to solve for the time variable. You'll use the amount of money accumulated, the principal amount, the annual interest rate, and the assumption that the interest is compounded annually. Plug these values into the formula to calculate the number of years.

You deposited $10,000 into a savings account at 6% interest. To determine how long it took for you to earn $4,800 in interest, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:

In this case, we can rearrange the formula to solve for t, because you want to find out how many years it took for your investment to turn into A = $10,000 + $4,800 = $14,800. Assuming the interest is compounded annually (n = 1), the formula becomes:

t = ln(A/P) / n * ln(1 + r/n)

Plugging in the numbers gives us:

t = ln($14,800 / $10,000) / ln(1 + 0.06)

By calculating this, you can get the number of years you had the money in the savings account.

Answer:

Step-by-step explanation:

area=4×22/7×14²=4×22×28=2464 units²

The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.

To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:

A = 4 * (22/7) * (14)²

A = 4 * (22/7) * 196

A = 4 * 22 * 28

A = 88 * 28

A = 2464

Thus, the surface area of the sphere is 2464 square units.

Answer:

the machine is mixing the nuts are not  in the ratio 5:2:2:1.

Step-by-step explanation:

Given that a machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1.

A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans.

Create hypotheses as

H0: Mixture is as per the ratio 5:2:2:1

Ha: Mixture is not as per the ratio

(Two tailed chi square test)

Expected values as per ratio are calculated as 5/10 of 500 and so on

Exp        250      100    100       50        500

Obs       269      112       74       45         500

O-E          19        -12      -26       -5           0

Chi          1.343   1.286  9.135   0.556   12.318

square

df = 3

p value = 0.00637

Since p value < alpha, we reject H0

i.e. ratio is not as per the given

We perform a chi-square goodness of fit test to analyze if the machine is mixing nuts according to the ratio. We set a null and alternate hypothesis, calculate expected frequencies for each group, calculate chi-square test statistic and compare it with the critical value. If the calculated chi-square is greater than the critical value, we reject the null hypothesis.

This question asks about hypothesis testing using chi-squared tests. In this particular case, we're testing the observed distribution of mixed nuts against the expected distribution given by the ratio 5:2:2:1.

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Answer:

Step-by-step explanation:

A continuous function is one that has a set of unique solutions. a function is also said to be continuous if at every interval, there exist no sudden change in the assumed values otherwise the function will be discontinuous.

for example, the sine and cosine function are continuous over a set of real integers.

from the question, any assumed expression of x and integrating over the interval x and infinity will render the function continuous.

Assumed f(x) = cuberoot of x

Integrating and evaluating will prove that the function is continuous, as such a defined function is always a continuous function and not necessarily lipschitz.

Answer:

B) 6 units

Step-by-step explanation:

The formula of the volume of the Pyramid is 1/3×area of the base×height

1/3×70×height=140

Dividing both sides by 70

1/3×height=2

Multiplying both sides by 3

Height = 6

Final answer:

The height of a right square pyramid with a rectangular base area of 70 square units and a volume of 140 cubic units is 6 units, by using the volume formula of the pyramid.

Explanation:

The question asks us to find the height of a right square pyramid with a given base area and volume. To find the height, we need to use the formula for the volume of a pyramid, which is given by the formula: Volume = (Base Area * Height) / 3. We are given the base area as 70 square units and the volume as 140 cubic units.

Using the formula to solve for the height we get:
Height = (Volume * 3) / Base Area = (140 * 3) / 70 = 6 units. Therefore, the height of the pyramid is 6 units.

Answer: Ballwin Bears

Step-by-step explanation:

Answer:

The Ballwin Bears are taller on average, and the Aviation Aces have players whose are more consistent.

Step-by-step explanation:

(This is the correct answer on Knewton-alta)

Answer:

E.) 1

Step-by-step explanation:

Firstly we will solve for L.H.S.

L.H.S. =[tex]Csc^2\theta[/tex]

Since we know that [tex]Csc^2\theta[/tex] is the inverse of [tex]Sin^2\theta[/tex].

So we can say that;

[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]

Now For R.H.S.

[tex]Cot^2\theta+1[/tex]

Since we  can rewrite [tex]cot^2\theta[/tex] as [tex]\frac{cos^2\theta}{sin^2\theta}[/tex].

Now we can say that the R.H.S. is;

[tex]\frac{cos^2\theta}{sin^2\theta}+1[/tex]

Now we add the fraction and get;

[tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}[/tex]

Now according to trigonometric identity;

[tex]cos^2\theta+sin^2\theta=1[/tex]

So, [tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}[/tex]

Here,

[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]   and     [tex]Cot^2\theta+1[/tex] = [tex]\frac{1}{sin^2\theta}[/tex]  

L.H.S. = R.H.S.

Hence [tex]csc^2\theta=cot^2\theta+1[/tex]

Answer:

The Teenagers spend $172.05 billion dollars in 2001.

Step-by-step explanation:

Given:

Number of billion dollars spent by teenagers in 2000 = $155

Percentage amount increase in 2001 = 11%

We need to find how many billions of dollars did teenagers spend in 2001.

Solution:

First we will find the Number of billion dollar increase in 2001.

Number of billion dollar increase in 2001 can be calculated by Percentage amount increase in 2001 multiplied by Number of billion dollar spent by teenagers in 2000 and then divided by 100.

framing in equation form we get;

Number of billion dollar  increase in 2001 = [tex]\frac{11}{100}\times 155 = \$17.05[/tex]

So no number of billion dollars teenagers spend in 2001 is equal to Number of billion dollars spent by teenagers in 2000 plus Number of billion dollar  increase in 2001 .

framing in equation form we get;

number of billion dollars teenagers spend in 2001 = [tex]\$155+\$17.05 = \$172.05[/tex]

Hence The Teenagers spend $172.05 billion dollars in 2001.

I'm not sure of whether or not you're aware of this, but you asked this question in the math section. Nevertheless, I remember in 5th grade I did a project on whether or not it is possible to use solar energy to heat up different colored bags filled with water, and to determine which one would heat up the quickest. If that one doesn't pique your interest, you can go to sciencebuddies.com and search through a variety of project ideas if you'd like. That's where I found mine.

Final answer:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. Students can collect cans with different types of food and predict which can will win a race down an inclined plane.

Explanation:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. In this experiment, students can collect several cans containing different types of food and predict which can will win the race down an inclined plane. They can then explain their prediction and see if it is correct. Another option is to collect empty cylindrical containers of the same size and fill them with different materials like wet or dry sand to see how it affects the race.

Answer:

the answer is 9/8 or 1 and 1/8

Step-by-step explanation:

divide 3/4 by 2 to get 3/8 and then multiply 3/8 by 3 (since its tripling) to get 9/8 which can also be written as 1 1/8. Hope this helps!

Answer:P(A/B)=0.08

Step-by-step explanation:

The probability formula to find p(A/B) is :

P(A/B) = p(A n B) / p(A)

Which means that B is contain in A and p(A n B) is p(B)

p(A n B)=p(B)=0.05

p(A)=0.625

Therefore

P(A/B) = p(A n B) / p(A)=p(B) / p(A)

P(A/B)=0.05 / 0.625

P(A/B)=0.08

The problem can be solved using combinatorics, specifically the permutation of a multiset. Using the formula P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is total number of operations and n1, n2,... are the number of each identical operation, the number of different possible sequences to complete the manufacturing operation are 35.

The number of sequences of the operations can be found by using the formula for permutations of multiset - a concept in combinatorics part of mathematics. Permutations of a multiset are the number of ways in which we can arrange all the elements of the multiset considering the repetition of elements. We have 7 operations in total: three identical notches (type A) and four identical bends (type B). The formula is:

P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is the total number of items(7 in this case), n1,n2,...,nk are the number of each type of item.

Therefore, the number of different possible sequences to complete the manufacturing is: P(7 ; 3, 4) = 7! / (3! * 4!). This evaluates to 35.

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Answer: d. Infinitely many solutions

Step-by-step explanation:

The given equation is expressed as

10-3x +10x-7 = 5x-5+2x+8

The first step is to make all the terms containing the variable to be on the left hand side of the equation and the constants to be on the right hand side of the equation.

10-3x +10x-7=5x-5+2x+8

10 - 7 + 10x - 3x = 5x + 2x - 5 + 8

7x + 3 = 7x + 3

Subtracting 7x and 3 from the left hand side and the right hand side of the equation, it becomes.

7x - 7x + 3 - 3 = 7x - 7x + 3 - 3

0 = 0

It has infinitely many solutions because as any value of x would satisfy both sides of the equation.

Answer:

$ 213.50

Step-by-step explanation:

From the question;

Albert spent;

We are required to determine Albert's monthly allowance;

Then;

Deducting $35.5, we get,

$(x/2 - 35.5)

Then, 3/5 of the remainder is on a book

Thus, 1 - 3/5 = 2/5 of the remainder (represents the amount that remained after buying a book and a shirt.

Therefore;

2/5 (x/2 - 35.5) = 28.5

We get;

x/2 - 35.5 = 28.5 (5/2)

x/2 - 35.5 = 71.25

 x/2 = 71.25 + 35.5

  x/2  = $ 106.75

    x = $ 106.75 × 2

       = $ 213.50

Therefore, Albert's monthly allowance is $ 213.50

Answer:

(5,-3) , (10, -2), (7,-8)

Step-by-step explanation:

The new triangle will be

(5,-3) , (10, -2), (7,-8) by mapping

(x,y) => (x +3, y-5)

Answer:

AB = 14 units

Step-by-step explanation:

Given:

A triangle GHJ with the following aspects:

A, B, C are midpoints of sides GH, HJ and GJ respectively.

AB = [tex]3x+8[/tex]

GJ = [tex]2x+24[/tex]

Midsegment Theorem:

The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and the length of the midsegment is one-half of the length of the third side.

Therefore, AB is the midsegment of sides GH and HJ and thus, is parallel to GJ and equal to one-half the length of GJ.

[tex]\therefore AB=\frac{1}{2}\times\ GJ[/tex]

Now, plug in the values of AB and Gj and solve for 'x'.

This gives,

[tex]3x+8=\frac{1}{2}(2x+24)\\\\3x+8=x+12\\\\3x-x=12-8\\\\2x=4\\\\x=\frac{4}{2}=2[/tex]

Now, the length of AB is given by plugging in 2 for 'x'.

[tex]AB=3\times2+8=6+8=14[/tex]

Therefore, the length of midsegment AB is 14 units.

Answer:

14 Units

Step-by-step explanation:

The length of midsegment AB is equal to one-half the length of side GJ. In this case, AB is given by the expression 3x + 8 and GJ is given by the expression 2x + 24.

To find the value of x, we can set the expressions for AB and GJ equal to each other and solve for x.

3x + 8 = 1/2(2x + 24)

We can simplify this equation by distributing the 1/2 to the terms inside the parentheses:

3x + 8 = x + 12

Next, we can subtract x from both sides to isolate the x term:

3x - x + 8 = 12

2x + 8 = 12

Then, we can subtract 8 from both sides:

2x = 4

Finally, we can solve for x by dividing both sides by 2:

x = 2

Now that we have the value of x, we can substitute it back into the expression for AB:

AB = 3(2) + 8

AB = 6 + 8

AB = 14

Therefore, the length of midsegment AB is 14 units.

Answer:

The population of city is 7 million in 2015.

Step-by-step explanation:

It is given that the population of a city, P, in millions, is a function of t, the number of years since 2010.

It means, P = f(t).  

We need to explain the meaning of the statement f(5) = 7 in terms of the population of this city.

f(5) = 7 means the population is 7 millions at t=5.

t = 5 means 5 years after 2010, i.e., 2010+5 = 2015

Therefore, the population of city is 7 million in 2015.

Answer:

Step-by-step explanation:

Answer: The equation that would help members to find how much they would pay per month is

40 + 12x = 460

Step-by-step explanation:

Let x represent the amount of money that members would pay per month.

Let y represent the number of months for which a member uses the gym.

There is a fee of $40 when you join, and the rest is paid monthly. This means that the cost of using the gym for x months would be

40 + xy

A one year membership to metro gym costs $460. Therefore are 12 months in a year. Therefore,

40 + 12x = 460

12x = 460 - 40 = 420

x = 420/12 = 35

The equation that would help members to find how much they would pay per month is

Answer:

The answer to your question is width = 8ab³

Step-by-step explanation:

Data

Area = 32a³b⁴ u²

length = 4a²b   u

Formula

Area of a rectangle = width x length

Solve for width

                           width = [tex]\frac{Area}{length}[/tex]

Substitution

                          width = [tex]\frac{32a^{3}b^{4}}{4a^{2}b}[/tex]

Simplify using rules of exponents, just remember that in a division we subtract the exponents and divide the coefficients normally.

                          width = 8 a²b³

Answer:

Step-by-step explanation: 32a^3 is -8 < a < - 8 axis interceptions 32a^3            vertical asymphotes None Extreme points of a32a^3 0,0

Answer:

Option A) inferential statistics        

Step-by-step explanation:

We describe inferential statistic as:

Inferential Statistic:

Thus, the correct answer is

Option A) inferential statistics.

Answer:

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

The figure in the question was split into the triangles in the attachment to the solution.

Now applying the principle of similar triangles, we have:

[tex]\frac{16}{x} = \frac{x}{9}[/tex]

cross-multiplying, we have:

[tex]x^{2} = 16*9 = 144[/tex]

solving for x,

x = 12

Answer:

Therefore, area under the curve is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

We have to find the area under curve y = x³ from 0 to 1 as limit.

Since Area 'A' = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x[/tex]

The given function is f(x) = x³

Since [tex]x_{i}=a+\triangle x.i[/tex]

Here a = 0 and [tex]\triangle x=\frac{1-0}{n}=\frac{1}{n}[/tex]

[tex]f(x_{i})=(\frac{i}{n})^{3}[/tex]

Now A = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x= \lim_{n \to \infty}\sum_{i=1}^{n}(\frac{i}{n})^{3}(\frac{1}{n})[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}\sum_{i=1}^{n}i^{3}[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}( \frac{n(n+1)}{2})^{2}[/tex]    Since 1³ + 2³ + 3³..............n³ = [tex][\frac{n(n+1)}{2}]^{2}[/tex]

[tex]= \lim_{n \to \infty}\frac{n^{2}(n+1)^{2}}{4n^{4}}[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{4}(1+\frac{1}{n})^{2}[/tex]

[tex]=\frac{1}{4}(1+0)[/tex]

[tex]=\frac{1}{4}[/tex]

Therefore, area under the curve is [tex]\frac{1}{4}[/tex]

Answer:

Casandra will run 8 miles on the 9th Day.

Step-by-step explanation:

Given:

Casandra on first day of training  she runs 4 miles

So we can say that;

[tex]a_1=4\ miles[/tex]

Also Given:

each day after that she adds on 0.5 mile.

So we can say that;

Common difference [tex]d=0.5\ miles[/tex]

We need to find on what day she will run 8 miles.

So we can say that;

[tex]T_n = 8[/tex]

Let the number of the day be denoted by 'n'

Solution:

Now By using the formula of Arithmetic Progression we get;

[tex]T_n= a_1+(n-1)d[/tex]

Now substituting the values we get;

[tex]8=4+(n-1)0.5[/tex]

Now by using distributive property we get;

[tex]8 =4+0.5n-0.5\\\\8=3.5+0.5n[/tex]

Now subtracting both side by 3.5 we get;

[tex]8-3.5=3.5+0.5n-3.5\\\\4.5=0.5n[/tex]

Dividing both side by 0.5 we get;

[tex]\frac{4.5}{0.5}=\frac{0.5n}{0.5}\\\\9=n[/tex]

Hence Casandra will run 8 miles on the 9th Day.

Answer: to suggest or accept that a theory or idea is true as a starting point for reasoning or discussion.

Step-by-step explanation:

Here's an example: Astronomers postulate that the comet will reappear in 4000 years.