Answer:

The batch of sweet should contain 4 lb of Brand A granola

The batch of sweet should contain 6 lb of Brand B granola

Explanations:Total amount of sweet items = 10 lb

Let the amount of brand A granola be x

Amount of brand B granola = 10 - x

Amount of nuts and dried fruits in the total sweet items = 22% of 10

Amount of nuts and dried fruits in the total sweet items = 0.22 x 10

**Amount of nuts and dried fruits in the total sweet items = 2.2lb**

Amount of nuts and dried fruits in brand A granola = 25% of x

**Amount of nuts and dried fruits in brand A granola = 0.25x**

Amount of nuts and dried fruits in brand B granola = 20% of (10-x)

**Amount of nuts and dried fruits in brand B granola = 0.2(10 - x)**

Amount of nuts and dried fruits in brand A granola + Amount of nuts and dried fruits in brand B granola = Amount of nuts and dried fruits in the total sweet items

**0.25x + 0.2(10 - x) = 2.2**

0.25x + 2 - 0.2x = 2.2

**Collect like terms**

0.25x - 0.2x = 2.2 - 2

0.05x = 0.2

x = 0.2 / 0.05

**x = 4 lb**

**The batch of sweet should contain 4 lb of Brand A granola**

**Amount of brand B granola = 10 - x**

Amount of brand B granola = 10 - 4

**Amount of brand B granola = 6 lb**

**The batch of sweet should contain 6 lb of Brand B granola**

Steve files head of household. In 2022, he received $23,000 in social security benefits, $10,000 in taxable retirement income, and $4,000 in interest and dividend income. Using the Social Security Benefits Worksheet - Line 6a and 6b, determine Steve's taxable social security benefits.

Steve's **taxable** social security benefits is** zero.**

Since** Steve **declares himself as the head of the home, his social security payments, which range from $25,000 to $34,000, will be subject to a 50% tax.

Retirement income,** interest income**, and** dividend** income are not considered social security benefits for determining the limit. Nevertheless, in the case at hand, the social security benefits total $23,000, which is less than the maximum of $25,000 and is thus not taxable.

As a result, Steve's Social Security** **benefits are **not taxable.**

Hence the taxable amount on Steve on **social security** benefits is Zero.

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2) Convert this fraction into a mixed number in lowest terms 60/25

Please I need step by step explanation.

The given **fraction** 60/25 into a **mixed number** would be 2 2/5 in the **lowest** terms.

A **fraction** is defined as a numerical representation of a part of a **whole** that represents a **rational** number.

First, we have to find the **whole number**,

Determine how many times the **denominator** enters the **numerator**. Divide 60 by 25 and preserve just the numbers to the left of the **decimal** point:

⇒ 60 / 25 = 2.4000 = 2

Then, find a new numerator :

**Multiply** the result by the denominator and **subtract** it from the original numerator.

⇒ 60 - (25 x 2) = 10

Now, put together

To obtain this, keep the original denominator and use the solutions from Steps 1 and 2:

⇒ 2 10/25 ⇒ 2 2/5

Thus, the given **fraction** 60/25 into a **mixed number** would be 2 2/5 in the **lowest** terms.

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Use the equation below and the indicated value to find an ordered pair that is a solution.

y=2x-1 Let x = 4.

The ordered pair is 4.

The **ordered pair** is 4 is 7.

An **equation **is a mathematical statement that is made up of two **expressions** connected by an equal sign. For example, 3x – 5 = 16 is an **equation**. Solving this equation, we get the value of the **variable** x as x = 7.

Given that,

The equation is

y = 2x-1

Substitute the value of x =4

y = 2x-1

y = 2×4-1

y = 7

The value of y at x = 4 is 7.

Hence, the ordered pair of 4 is 7.

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Put 3/4, -1/2, -1/4 in order from least to greatest.

**Answer:**

**-1/2, -1/4, 3/4.**

**Explanation:**

If we draw the number in a number line, we get:

So, if we order them from least to greatest, we get:

-1/2, -1/4, 3/4.

**Answer:**

-1/2, -1/4, 3/4

**Step-by-step explanation:**

M=W(1+rt) (solve the following formula for "t"

Given the following formula given in the exercise:

[tex]M=W\mleft(1+rt\mright)[/tex]You can solve for the variable "t" by following the steps shown below:

1. You must apply the Disrtributive proprerty on the right side of the equation:

[tex]\begin{gathered} M=(W)\mleft(1)+(W)(rt\mright) \\ M=W+Wrt \end{gathered}[/tex]2. Now you need to apply the Subtraction property of equality by subtracting "W" from both sides of the equation:

[tex]\begin{gathered} M-(W)=W+rtW-(W) \\ M-W=Wrt \end{gathered}[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by "Wr":

[tex]\begin{gathered} \frac{M-W}{Wr}=\frac{Wrt}{Wr} \\ \\ t=\frac{M-W}{Wr} \end{gathered}[/tex]**The answer is:**

The hypotenuse of right triangle XYZ is 28 and m

**Solution**

For this case we can do the following:

**m < X = 60**

**One angle in a right triangle needs to be 90º**

So then we can find the measure of the other angle like this.

**180 -90-60 = 30º**

We can find the following identity:

[tex]\sin 60=\frac{y}{28}[/tex]And solving for thw leg opposite we got:

[tex]y=28\cdot\sin 60=24.25[/tex]

find inverse of function f(x)=3/x+2

The answer is either 3/ x-2 or 3/x -2

What are the dimensions of the rectangle with Maximum area?

Let x be the length of the rectangle and y be the width of the rectangle, then we can set the following equations:

[tex]\begin{gathered} 2x+2y=40, \\ A=x\cdot y\text{.} \end{gathered}[/tex]Solving the first equation for x we get:

[tex]\begin{gathered} 2x=40-2y, \\ x=\frac{40}{2}-\frac{2y}{2}, \\ x=20-y\text{.} \end{gathered}[/tex]Substituting x=20-y in the second equation we get:

[tex]\begin{gathered} A=(20-y)\times y, \\ A=20y-y^2. \end{gathered}[/tex]Now, we will use the first and second derivative criteria to find the maximum.

The first and second derivatives are:

[tex]\begin{gathered} A^{\prime}(y)=20-2y. \\ A^{\prime\prime}(y)=-2. \end{gathered}[/tex]Since the second derivative is a negative number that means that A(y) reaches a maximum when A´(y)=0.

Solving A´(y)=0 for y we get:

[tex]\begin{gathered} 20-2y=0, \\ 20=2y, \\ 10=y\text{.} \end{gathered}[/tex]Now, substituting y=10 in x=20-y, we get:

[tex]x=20-10=10.[/tex]**Answer:**

Length 10 yards.

Width 10 yards.

can you solve 3 5/12 + 1 3/8 ?

**Answer:**

**4 19/24**

**Explanation:**

First, we need to convert the mixed numbers into a fraction, so:

[tex]\begin{gathered} 3\frac{5}{12}=\frac{3\times12+5}{12}=\frac{36+5}{12}=\frac{41}{12} \\ 1\frac{3}{8}=\frac{1\times8+3}{8}=\frac{8+3}{8}=\frac{11}{8} \end{gathered}[/tex]Then, we can add the fractions as follows:

[tex]\frac{41}{12}+\frac{11}{8}=\frac{41(8)+12(11)}{12(8)}=\frac{328+132}{96}=\frac{460}{96}[/tex]Finally, we can simplify the fraction and write the fraction as a mixed number as:

[tex]\frac{460}{96}=\frac{460\div4}{96\div4}=\frac{115}{24}[/tex][tex]\frac{115}{24}=4\frac{19}{24}[/tex]Because when we divide 115 by 24, we get 4 as a quotient and 19 as a remainder.

Therefore, the answer is: 4 19/24

The weights of a certain brand of candies are normally distributed with a mean weight of 0.8543 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 469 candies, and the package label stated that the net weight is 400.3 g. (If every package has 469 candies, the mean weight of the candies must exceed

400.3

469=0.8536 g for the net contents to weigh at least 400.3 g.)

A randomly chosen candy has a** probability **P=0.4992 of weighing at least 0.8536 g.A sample of 441 candies chosen at random has a probability P=0.3712 of having an average weight of at least 0.8543 g.Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to customers on the label needs to be reevaluated.** z-score** can be used to determine the likelihood that an element has a weight greater than 0.8536** sample** now has n=441 candies and we want to know the likelihood that the mean weight is at least 0.8543 g:

Given,

The weight of candies normally distributed ;

Mean weight of candies = 0.8543 g

**Standard deviation**, σ = 0.0519 g

Sample of candy came from a packet of 469 candies

Net weight of the packet = 400.3 g

Average weight of the candies in the packet;

[tex]x_{avg} =[/tex] ∑xi/n = 400.3/469 = 0.8535

The population standard deviation (sigma=0.0519 g) is the standard deviation for a confectionery that was chosen at random (sample size n=1).

Thez = (X - μ) / (σ/√n) = (0.8536 - 0.8535) / (0.0519/√1) = 0.0001/0.0519 = 0.002

P(X > 0.8536) = P(z > 0.002) = 0.4992

A randomly chosen candy has a probability P=0.4992 of weighing at least 0.8536 g.

The z-score needs to be computed if thez = (X - μ) / (σ/√n) = (0.8543 - 0.8535) / (0.0519/√441) = 0.0008/0.0024 = 0.3288

P(X > 0.8543) = P(z > 0.3288) = 0.37115

A sample of 441 candies chosen at random has a probability P=0.3712 of having an **average weight** of at least 0.8543 g.

z = (X - μ) / (σ/√n) = (0.8556 - 0.8535) / (0.0519/√469) = 0.0021/0.0024 = 0.89

P(X > 0.8556) = P(z > 0.89) = 0.18673

Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to** customers** on the label needs to be reevaluated.

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Is (-2,-6) a solution to the equation y = 3x?

Oyes

Ono

**Answer:**

**yes**

**Step-by-step explanation:**

if y = -6,

3x = -6

x = -2

**Answer:**

yes

**Step-by-step explanation:**

y = 3x?

Let x = -2 and y = -6

-6 = 3(-2)

-6 = -6

This is a true statement so (-2,-6) is a **solution to the equation** y = 3x

The number of students in the tutoring center was recorded for 27 randomly selected times. The data is summarized in the frequency table below. What is the class width for this frequency distribution table

The **class width** for this frequency table is 5.

The class width is described as the distance between the** lower class** of two consecutive classes.

One can calculate class width by finding the difference between the two consecutive** lower classes.**

In the figure above, the first two classes are described as

0-4

5-9

So, the** lower classes** of these intervals are 0,5

Thus the difference between them is 5

Therefore, the **class width** for this** frequency distribution table** is 5.

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Write an inequality that represents the graph below

An** inequality** that represents the given** graph** is; 2 < x < ∞.

For the given question.

The** inequality** is given by the values of the **number line.**

The value is starting from 2 and goes up to infinity.

But, It is a hollow dot at 2 means 2 is with **open interval, **as 2 will not be taken for the value of x.

The values lies between, (2, ∞)

Thus, the inequality that represents the given** graph **is; 2 < x < ∞.

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What is 372.7332 rounded to the nearest thousandth?

Please help rn I have until 3pm

372.733 i tjink thats the asnwer

Find the critical value (tα/2) for a 99% confidence interval if the sample size is 15. Round your answer to three decimal places.

tα/2 =

The **critical value **(tα/2) for a 99% **confidence **interval for the sample size 15 is 2.977 .

We have to find the **critical value** tα/2 for 99% confidence interval, we are given the **sample size**.

First we will find the **alpha value** to get the critical value.

=100%-99%

=1-0.99

=0.01

α=0.01

α/2=0.01/2

α/2=0.005

degrees of freedom(df)= n-1=15-1=14

We will use degrees of freedom and α/2 values to find the **critical value** that is tα/2.

By using the **t table** we get the critical value of tα/2=2.977.

Therefore, the **critical value** for 99% confidence interval with sample size 15 is 2.977.

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Which equation represents a horizontal line that passes through the point (2, 7)? А x=2 В y = 2 C X= 7 D y=7

It is important to know that horizontal lines are represented by the equation y = k, where k is a real numbers.

In this case, if the equation passes thorugh (2,7), then the equation would be y = 7.

Hence, the answer is D.In isosceles △ABC where AC≅BC, altitiude CD is drawn. If AC= 17 and AB= 30. Determine the altitiude of the triangle.

By definition, an Isosceles triangle is a triangle that have two congruent sides, and the altitude divides the triangle into two equal Right triangles.

Remember that a Right triangle is a triangle that has an angle whose measure is 90 degrees.

Based on this, you know that:

[tex]\begin{gathered} AD=BD=\frac{AB}{2} \\ \\ AC=BC \end{gathered}[/tex]Knowing that:

[tex]\begin{gathered} AB=30 \\ AC=17 \end{gathered}[/tex]You get that:

[tex]\begin{gathered} AD=BD=\frac{30}{2}=15 \\ \\ AC=BC=17 \end{gathered}[/tex]The Pythagorean Theorem states that:

[tex]a^2=b^2+c^2[/tex]Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

So you can identify that, for this case:

[tex]\begin{gathered} a=17 \\ b=15 \\ c=CD \end{gathered}[/tex]Where "CD" is the altitude of the triangle.

Therefore, substituting values and solving for "CD", you get this result:

[tex]\begin{gathered} 17^2=15^2+CD^2 \\ \sqrt[]{17^2-15^2}=CD \\ CD=8 \end{gathered}[/tex]**The answer is: Option (1)**

Sun lei bought a computer for $1800. The total cost, including tax, came to $1890. What is the tax rate?

Given:

Cost of computer without tax $1800.

Total cost including tax is $1890

[tex]\text{Tax amount =1890-1800}[/tex][tex]\text{Tax amount = \$90}[/tex]Let the tax rate be x

[tex]90=1800\times\frac{x}{100}[/tex][tex]\frac{90}{18}=x[/tex][tex]x=5[/tex]**Tax rate is 5%**

CD is the mid segment of trapezoid WXYZ.-What is the value of X?-What is XY?-What is WZ?

The midsegment theorem states that the length of the midsegment is equal to half the length of the base. From the information given,

midsegment = CD = 22

base = XY = 4x + 1

By applying the midsegment theorem, we have

CD = 1/2XY

22 = 1/2(4x + 1)

By crossmultiplying, we have

22 * 2 = 4x + 1

44 = 4x + 1

4x = 44 - 1

4x = 43

x = 43/4

**x = 10.75**

Thus,

Substituting x = 10.75 into XY = 4x + 1, it becomes

XY = 4(10.75) + 1

XY = 43 + 1

**XY = 44**

Substituting x = 10.75 into WZ = x + 3, it becomes

WZ = 10.75 + 3

**WZ = 13.75**

Nandita earned 224 dollars last month. she earned 28 dollars by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars Nandita earned last month by babysitting.

the selling price of each card is = 28 $

let she sold x number of cards,

so, the equation is,

28x = 224

x = 224/28

x = 8

**thus, the answer is number of cards sold by nandita is 8 **

**so, the equation is **

**28x = 224 **

8.26×10^0 scientific notation or standarn form

The number** 8.26 10^0 ** is shown in **scientific notation**.

**Its standrad form is: 8.26 ** since we know that any base different from zero raised to the power "0" (zero) gives "1" (one).

Determine the open intervals on which the function is increasing, decreasing, or constant.(Enter your answers using interval notation. If an answer does not exist, enter DNE.)

**Given:**

**To find:**

The interval at which the function is increasing, decreasing and constant.

**Explanation:**

We know that,

For a function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function.

For a function, y = F(x), if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.

According to the graph,

The function is increasing in the interval,

[tex][2,\infty)[/tex]Because, if x increases from 2, the value of y increases.

The function is decreasing in the interval,

[tex](-\infty,-2][/tex]Because, if x increases from negative infinity, the value of y decreases.

As we know, a constant function is a function whose output value is the same for every input value.

Here, the function is not constant at any of the intervals.

**Final answer:**

**Increasing**:

**Decreasing**:

**Constant**: DNE.

I am having trouble with the last two questions. I worked through finding the slope and y-intercept with a previous tutor, before we got disconnected.6. Express this equation as a function D of P and find its domain.7. How many shirts per month will be demanded if the price is $27?

*Data:*

*Equation as a function of D of P*

**Answer (6):**

• Domain

[tex](-\infty,+\infty)[/tex]To know how many shirts per month will be demanded if the price is $27, we have to use *P = $27:*

**Answer (7): $37.80**

If f(x)=√x and g(x)= - 2x+3, find (f . g)(x) and (g . f)(x).

(f . g)(x)=_____

(Simplify your answer. Type an exact answer, using radicals as needed.)

Thee **values **of the functions are;

(f . g)(x) = √(-2x + 3)

(g . f)(x) = - 2√x + 3

What is a function?A **function** can simply be defined as a law, rule or expression showing the **relationship** between two variables in an equation or expression.

The two variables are given;

The dependent variableThe independent variableGiven the functions;

f(x)=√x g(x)= - 2x+3To determine the function (f . g)(x), substitute the value of x as g(x) in the function, we have;

(f . g)(x) = √(-2x + 3)

To determine the function (g . f)(x), substitute the values of x in the function g(x), we have;

(g . f)(x) = - 2√x + 3

Hence, the **functions **are √(-2x + 3) and - 2√x + 3

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17. The rent for a store is GH¢420.00 a year.

What is the rent for the store in six

months?

**Answer:**

**Step-by-step explanation:**

The rent is **420 **a year.

6 months is** half a year**.

The rent for 6 months is **half the rent for a year**:

Find the solution to the system of equations represented by the matrix shownbelow.83-161E441371-63ХUse the operation buttons to start solving

The solution to the system of **equations **represented by the** matrix **is (x, y, z) = (6, 7, 6).

Maybe your matrix is ...

[tex]$\left[\begin{array}{ccc|c}3 & -1 & 7 & 53 \\ 1 & 7 & 1 & 61 \\ 9 & 1 & 1 & 67\end{array}\right]$[/tex]

A calculator can tell you the **solution **is ...

(x, y, z) = (6, 7, 6)

The third **variable** in systems of equations with more than two variables can be defined in terms of the other two (as for solution by substitution). This can be used to create two equations with two unknowns by substituting it into the remaining **equations**. The value of the third variable can then be determined using that answer. The use of this **technology** is demonstrated in the attached.

The last equation served as a definition, which was then applied to the first two equations. An **algebraic solution **can be solved using the same strategy.

The answer is (x, y, and z) = (6, 7, 6).

Complete question: Find the solution to the system of equations represented by the matrix shown below. 3 -1 7 53 1 7 1 61 9 1 1 67

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Rotate this hexagon 180º.

(0, -8)

(3, -8)

(6,-5)

(6, 1)

(3, 2)

(0, 2)

After rotation the **coordinates** of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)

Upon **rotation of this hexagon** by 180

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .

After rotation, the co- ordinates change from

(0, -8) → (0, 8)

(3, -8) → (-3, 8)

(6,-5) → (-6, 5)

(6, 1) → (-6, -1)

(3, 2) → (-3, -2)

(0, 2) → (0, -2)

Therefore, after rotation the **coordinates of the hexagon **is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)

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A train travels 150 km in 2 hours and 30 minutes. What is its average speed?

**Answer:**

It's average speed is 48 km per hour

**Step-by-step explanation:**

**Answer:**

60 km/hr

**Step-by-step explanation:**

150 km / 2.5 hr = 60 km/hr

I need help with this question parts a - e

**Given:**

650 lb of coffee is sold when the price is $4 per pound,

400 lb of coffee is sold at $8 per pound.

**To find:**

A) List the data points

B) The slope of line joining the points

C) Interpretation of meaning of slope of line

D) linear equation of data using point slope form

E) Using the function we need to predict the number of consumers buying at $6 per pound

**Step-by-step solution:**

**A) Data points of the given data:**

Data points:

(4,650) and (8,400)

**B) The slope of the line joining the points:**

**C) Interpretation of meaning of slope of line:**

Slope here means that:

When there is an increase in the price of coffee then the weight of coffee decreases.

Weight per dollar of coffee decreases at the rate of 62.5

**D) linear equation of data using the point-slope form:**

Applying point-slope form:

y - y1 = m(x - x1)

y - 650 = -62.5(x - 4)

y = -62.5x + 900

In function notation it can be represented as:

S(P) = -62.5P + 900

**E) Using the function we need to predict the number of consumers buying at $6 per pound**

To predict that, we will simply put the value of P equal to 6 in the given function:

S(P) = -62.5P + 900 At P = 6

S(P) = -62.5(6) + 900

S(P) = 525

Thus we can say that 525 customers will buy at $6 per pound.

The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020? Explain your answers.

Given the function of the rate of change of the population:

[tex]P(t)=200e^{0.02t}[/tex]**The integral of this function will be the value of the population growth of the town from 1990 to 2010. This is because P(t) is the rate of change of population, its integral will be the antiderivative, that is the population of the town.**

To calculate the change in population we have to find the integral from 5 to 10 of P(t):

[tex]\begin{gathered} \int_5^{10}200e^{0.02t}dt \\ 200\int_5^{10}e^{0.02t}dt \\ 200\cdot\frac{e^{0.02t}}{0.02} \\ 10000e^{0.02t} \\ (10000e^{0.02(10)})-(10000e^{0.02(5)}) \\ 1162.3 \end{gathered}[/tex]**The change in population can not be a decimal number, so we can round it to 1162.**

To calculate the population in 2020 we have to find the integral from 0 to 30 of P(t) and then add it to 10000 which was the initial population (we already know the integral so we're just going to evaluate it):

[tex]\begin{gathered} 10000e^{0.02(30)}-10000e^{0.02(0)} \\ 8221.2 \\ 10000+8221.2=18221.2 \end{gathered}[/tex]**It means that the population in 2020 is 18221** (Remember that we round it because it is not possible to have a decimal value for the population of the town).

16. one of the driving reasons behind the need for data management is to manage risk associated with the misstatement of financial data. true or false?
Max's bedroom is rectangular shaped and has a total areaof 140 square feet. If the short wall is at 10 feet long,what is the length of the longer wall?
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"How can an understanding of thenumber properties help you to solveequations that represent real-worldsituations?"
X-3 is a factor of x+ax2x+3
What are sustainable use practices?A any materials that exist in nature and that are used by humansB the managed consumption of natural resources to prevent their depletion or environmental destructionC the deployment of fossil fuels to environments that previously did not have access to such resourcesD ways in which individuals are able to conserve native animal and plant species
Help! Help! 9261 divided by 57
Determine the unknown angle in the triangle pictured below:
What is a scanning tunneling microscope?An instrument used to view cells and bacteria.An instrument used to view viruses.An instrument used for imaging surfaces at the atomic level.An instrument used to view quarks.
George found that he blinked 85 times in 15 minutes. At this rate, how many seconds passed during the 51 blinks?
Which represents the equation 6x+3y= 12 whO y=-2x+4O y = 2x+4Oy=-2x-4O y=2x-4