The sum of two numbers is 28. The first number is 7 more than twice the second number. Let a represent the first number. Let b represent the second number. What is the second number? Use the table to guess and check. Two Numbers a b a + b = 28 Check a = 2 b + 7

Answer:

3,256bulbs

Step-by-step explanation:

From the question, we can see that;

Total number of boxes ordered = 22boxes

If each box contains 148 bulbs, then;

1 box = 148bulbs

To get the total bulbs we have we will say;

22boxes = x bulbs

solve this two expressions for x:

1box = 148bulbs

22boxes = x bulbs

Cross multiply

1×x = 22×148

x = 3256bulbs

Hence the best estimate of the total number of bulbs the store orders is 3,256bulbs

Answer:

Step-by-step explanation:

Answer:

3,256bulbs

Step-by-step explanation:

From the question, we can see that;

Total number of boxes ordered = 22boxes

If each box contains 148 bulbs, then;

1 box = 148bulbs

To get the total bulbs we have we will say;

22boxes = x bulbs

solve this two expressions for x:

1box = 148bulbs

22boxes = x bulbs

Cross multiply

1×x = 22×148

x = 3256bulbs

Hence the best estimate of the total number of bulbs the store orders is 3,256bulbs

The correct answer is (j - k)(x) = 10 + x.

To find the difference in the amount of money between Joel's and Kevin's accounts, we subtract the value of Kevin's account (k(x)) from Joel's account (j(x)).

(j - k)(x) = (25 + 3x) - (15 + 2x)

            = 25 - 15 + 3x - 2x

            = 10 + x

This expression represents how much more money is in Joel's account compared to Kevin's account after x weeks.

Therefore, the correct function is (j - k)(x) = 10 + x.

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Answer:

C. 4, -2 1/2

Step-by-step explanation:

(x,y)

its kinda easy

Step 1

Draw the triangle involving the diagonal of the TV

The algebraic expression of raise t to the 10th power then add the result to 3 is t¹⁰ + 3

An algebraic expression is an expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, multiplication, exponent, etc.

Given: raise t to the 10th power then add the result to 3

Note: t is the variable here

Let's write algebraic expression now:

raise t to the 10th power => t¹⁰

then add the result to 3 => t¹⁰ + 3

Therefore, the algebraic expression is t¹⁰ + 3

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Answer:

  f(x) = (x +6)(x -5)  or  f(x) = x² +x -30

Step-by-step explanation:

You want a quadratic function whose zeros are -6 and +5.

If p is a zero of the polynomial f(x), then (x-p) is a factor. The two given zeros meant that the factors are ...

  f(x) = (x -(-6))·(x -5)

  f(x) = (x +6)(x -5) . . . . . . . . simplify a bit

This can be put in standard form by multiplying the factors:

  f(x) = x(x -5) +6(x -5) = x² -5x +6x -30

  f(x) = x² +x -30 . . . . . . . . simplified quadratic function

The quadratic function of the zeros is f(x) = \(x^2+x-30\).

What is quadratic function?

A polynomial function that has one or more variables and a variable having a maximum exponent of two is said to be quadratic. A polynomial of degree 2 is referred to as such because the greatest degree term in a quadratic function is of second degree. There must be at least one second-degree term in a quadratic function. It is a mathematical function.

Here the zeros of the function is -6 and 5.

We know that if zeros of the function is a then the factor is (x-a).

Then,

=> f(x) = (x-(-6))(x-5)

=> f(x) = (x+6)(x-5)

=> f(x) = \(x^2+6x-5x-30\)

=> f(x) = \(x^2+x-30\)

Hence the quadradic function is f(x) = \(x^2+x-30\).

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Answer:

To factor any expression, find the greatest common factor that all of the terms share. In this case, we have: 4p^2, 5pq, and -6pq^2.

We see that the only common factor they share is "p".

So, we take out p to get: p(4p+5q-6q^2), which is our answer, since this can't be simplified further.

Let me know if this helps!

Answer:

4p²+5pq-6pq²

taking common

p(4p+5q-6q²)

Answer:

multiple it and then when you get your answer times them

Answer: 0, 5

Step-by-step explanation: a translation is just like sliding the object in this case a triangle/point on the triangle. so the point it is at now is -2, 5 because it is 2 to the left and 5 up. and if you go to the right 2. then you are adding 2 to the x value. so -2 +2 = 0. which is how you get 0, 5

Answer:

18.9c - 11.2d + 9.3f

Step-by-step explanation:

First, write the equation as adding all the parentheses together like so:

(9.7c - 1.9d) + (9.2c + 1.1f) + (8.2f - 9.3d)

Remove the parentheses:

9.7c - 1.9d + 9.2c + 1.1f + 8.2f - 9.3d

Collect like terms (9.7c and + 9.2c):

18.9c - 1.9d + 1.1f + 8.2f - 9.3d

Collect like terms again (1.9d and - 9.3d):

18.9c - 11.2d + 1.1f + 8.2f

Collect like terms again (1.1f + 8.2f)

18.9c - 11.2d + 9.3f

Hope this helped!

Answer:

D) 14

Step-by-step explanation:

Absolute value |x| is defined as the distance x from 0.

Basically, whatever is in the absolute value sign cannot be negative

Answer:

75%

Step-by-step explanation:

Divide 42 and 56

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer:

44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question, we have that:

\(p = 0.211, n = 40\)

So

\(\mu = 0.211, s = \sqrt{\frac{0.211*0.789}{40}} = 0.0645\)

What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

This is 1 subtracted by the pvalue of Z when X = 22. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.22 - 0.211}{0.0645}\)

\(Z = 0.14\)

\(Z = 0.14\) has a pvalue of 0.5557

1 - 0.5557 = 0.4443

44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

Answer:

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

Step-by-step explanation:

Proportion of all children in the United States who currently live with at least one grandparent is higher than 11%

This means that the null hypothesis is:

\(H_0: p = 0.11\)

And the alternate hypothesis is:

\(H_a: p > 0.11\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.11 is tested at the null hypothesis:

This means that \(\mu = 0.11, \sigma = \sqrt{0.11*0.89}\)

Suppose that in a recent sample of 1550 children, 214 were found to be living with at least one grandparent.

This means that:

\(n = 1550, X = \frac{214}{1550} = 0.1381\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.1381 - 0.11}{\frac{\sqrt{0.11*0.89}}{\sqrt{1550}}}\)

\(z = 3.54\)

Pvalue of the test and decision:

This is the probability of finding a sample proportion above 0.1381, which is 1 subtracted by the pvalue of Z = 3.54.

\(z = 3.54\) has a pvalue of 0.9999

1 - 0.9999 = 0.0001

The pvalue of the test is 0.0001 < 0.02, which means that we reject the null hypothesis and accept the alternate hypohteis that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The length of the side b is 106. 7 inches

The Pythagorean theorem can be defined as a mathematical theorem stating that the square of the longest side of a given triangle, called the hypotenuse side is equal to the sum of the square values of the other two sides.

This is represented as;

x² = y² + z²

Such that;

Now, substitute the values

121² = 57² + b²

find the squares

b² = 14, 641 - 3249

b = √11392

b = 106. 7 inches

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Answer:

Step-by-step explanation:

The area of a triangle is 1/2 of the base of the triangle multiplied by the height.

8.7/2 = 4.35

4.35 x 4.5 = 19.575

The answer is 19.575 ft²

The total measure of angles in a triangle is 180°.

3x° + 2x° + 4x° = 180°

9x° = 180°

x° = 180° ÷ 9

x° = 20

Our 3 angles are:

3(20) = 60°

2(20) = 40°

4(20) = 80°

Done.

Answer:

Step-by-step explanation:

3x+2x+4x=180

9x=180

x=180/9=20

3x=3×20=60°

2x=2×20=40°

4x=4×20=80°

Answer:

5.61

Step-by-step explanation:

66/22 = 3

3×1.87 = 5.61

Answer:

There was an association between extracurricular participation and grades, but it's not necessarily a causal relationship.

Step-by-step explanation:

This was an observational study since students were not randomly assigned to treatment groups—so we can say that there is an association or a relationship extracurricular participation and grades. Since this wasn't an experiment, we don't necessarily know that extracurricular participation caused higher grades.

Activities in which students participated in sports benefit in a variety of ways, including greater grades and test scores, higher academic achievements, more regularity in class attendance, and an increase in self.

There had been a link between extracurricular involvement and grades, but there was not definitely a causal relationship, thus they cannot make any conclusions from this research.

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Answer:

I'm pretty sure the answer is 21/20 or 1.05

Answer:

☆This is because ascending, not descending when looking on a graph.

☆The slope's number is a positive number.

This is oddly the funniest question I've seen so far. But never fear, I guess I'm here? :\

Honestly, I'm kinda lost but your answer should be $88.88. Even though it would say $88.88 multiplied by total hours, which is 4 hours and 25 minutes is $377.74, that answer is determined by a thousandth of a number. If you want it the other way, it's 88.8824.

Definitely hope this helped. [Pretty much, the answer is $88.88.]

The cost of labor per hour is $75.

It is required to find the cost of labor per hour.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The total amount that the technician charged her is the sum of the cost for the total hours worked and the costs of the parts.

Total charge = cost of total hours worked + cost of parts

$377.75 = $59 +  cost of total hours worked

Cost of total hours worked = $377.75 - $59

Cost of total hours worked = $318.75

In order to determine the cost per hour of labor, divide the total cost of total hours worked by the hours worked.

$318.75 / 4.25 = $75.

Therefore, the cost of labor per hour is $75.

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You need to set aside each month for an emergency fund and the retirement amount is $970.

An emergency fund is separate savings account to cater to the following unplanned situations:

It is prudent to have up to 6 months' salary in an emergency fund.

Monthly salary = $2,650

Monthly expenses = $1,465

Emergency fund = 30% of expenses

= $440 ($1,465 x 30%)

Retirement savings = 20% of the salary

= $530 ($2,650 x 20%)

Total amount to set aside each month = $970 ($440 + $530)

Thus, for your retirement and emergency fund, you need to set aside $970 monthly.

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