Mean of 6 numbers is 41. Remove one number and the mean of the five numbers is 46. What is the unknown number

A solution would be:

[tex](1,32)[/tex]

This is a linear equation written in Slope-Intercept form. Recall that this form, in general, is written as follows:

[tex]y=mx+b \\ \\ \\ Where: \\ \\ m:slope \\ \\ b:y-intercept[/tex]

In this case, we have the following equation:

[tex]y=-4x+36 \\ \\ \\ Where: \\ \\ m=-4 \\ \\ b=36[/tex]

In order to find a solution, let's set [tex]x=1[/tex], so the y-value will be:

[tex]y=-4(1)+36 \\ \\ y=-4+36 \\ \\ y=32[/tex]

So, a  solution to the linear equation is the point [tex](1,32)[/tex]

Final answer:

The solutions to y = -4x + 36 are x = 3 resulting in y = 24, and x = -7 resulting in y = 64, both of which have been verified to be correct by substitution back into the original equation.

Explanation:

To find a solution to the linear equation y = -4x + 36, we can substitute any value for x and solve for y, or vice versa. Let's use the given solutions x = 3 and x = -7 to find the corresponding values for y.

Substitute x = 3 into the equation: y = -4(3) + 36, which simplifies to y = -12 + 36, resulting in y = 24.

Substitute x = -7 into the equation: y = -4(-7) + 36, which simplifies to y = 28 + 36, resulting in y = 64.

To check the validity of these solutions, we back-substitute them into the original equation. For x = 3, the equation becomes 24 = -4(3) + 36, which simplifies to 24 = 24, confirming the first solution. Similarly, for x = -7, the equation becomes 64 = -4(-7) + 36, simplifying to 64 = 64, confirming the second solution. Both substitutions lead to an identity, verifying the correctness of the solutions.

Answer: 0.1

Step-by-step explanation: you only need to add zero to the first value,

for example if you have 1/10, you add zero, getting the next equation

10/10 if you add a zero to value you can add a zero to the result getting the following result

10/10=0. in this point both values are divisible

and 10 between 10 is equal to 1

as you finish add zeros you can add a point and after the 1 getting this result

1/10 = 0.1

The cost of one roll of plain wrapping paper is found to be $10, and one roll of holiday wrapping paper is $18.

We have two equations based on the given information:

Emily's sales: 14 rolls of plain wrapping paper + 6 rolls of holiday wrapping paper = $248

Joe's sales: 10 rolls of plain wrapping paper + 12 rolls of holiday wrapping paper = $316

Using algebra to solve the system, we represent the cost of one roll of plain wrapping paper as p, and the cost of one roll of holiday wrapping paper as h. Thus, the equations become:

14p + 6h = 248

10p + 12h = 316

We use the method of substitution or elimination to find the value of p and h. For instance, using elimination, we can multiply the first equation by 2 to make the coefficients of h the same:

(14p + 6h) * 2 = 248 * 2

28p + 12h = 496

Then we subtract the second equation from this new equation:

(28p + 12h) - (10p + 12h) = 496 - 316

18p = 180

p = $10

With the cost of plain wrapping paper found, substitute p = $10 into one of the original equations to find h:

10 * 10 + 12h = 316

12h = 216

h = $18

The cost of one roll of plain wrapping paper is $10, and the cost of one roll of holiday wrapping paper is $18.

Answer:

$12.80

Step-by-step explanation:

Sara bought 4 pounds of coffee.

Each pound (lb) costs $3.20

To find the total cost, multiply the cost per pound ($3.20) with the amount of pounds Sara is going to buy (4):

4 x 3.20 = $12.80

$12.80 would be the total cost before tax.

~

Answer:

12.8

Step-by-step explanation:

Its proportions: 1 pound equals 3.20, 4 poundes equals x.

3.20 (cost per pound) x 4 (how many pounds) = 12.8 (answer)

Answer:

45 less than twice a number is 5 times that number

Step-by-step explanation:

n = 15

Use one of the four fundamental arithmetic operations to add, subtract, multiply, or divide two or more integers. For challenging computations, we use the PEMDAS approach.

Given five times n is equals to 45 less than twice the number of n.

hence,

5 * n = 2* n + 45

3* n = 45

n = 15

Therefore the value of the n in the given problem is 15.

Learn more about Arithmetic operations here:

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Answer:

No, because the two shorter sides added must be longer than the longest side.

Also 1 squared plus 2 squared is not equal to 5 squared.

Answer:

A credit score is a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual. A credit score is primarily based on a credit report, information typically sourced from credit bureaus.

Answer:

a number assigned to a person that indicates to lenders their capacity to repay a loan.

Step-by-step explanation:

The cofunction of cos is sin(90-x)

90 degrees is equal to PI/2

The cofunction becomes sin(PI/2 - 2PI/9)

Rewrite both fractions to have a common denominator:

PI/2 = 9PI/18

2PI/9 = 4PI/18

Now you have sin(9PI/18 - 4PI/18)

Simplify:

Sin(5PI/18)

The cofunction of cos 2pi/9 is sin(pi/2 - 2pi/9), which is a basic concept in trigonometry.

The student is asking about the cofunction of

cos 2pi/9

. In trigonometry, the cofunction of a function is basically the complementary function of 90 degrees minus the original function. In this case, the cofunction of cos is sin, so to find the cofunction of cos 2pi/9, you need to find sin(90 - 2pi/9). However, since we are dealing with radians here, rather than degrees, we will be using pi/2 instead of 90 degrees. Therefore, the cofunction of cos 2pi/9 is

sin(pi/2 - 2pi/9)

.

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Answer:

The price of the almonds is $0.38 per pound.

Step-by-step explanation:

Gabby measures out 55 pounds of almonds at the grocery store bulk section.

At checkout the total cost is $20.90.

So, the price per pound will be = [tex]\frac{20.90}{55}[/tex]

= $0.38 per pound.

Therefore, the price of the almonds is $0.38 per pound.

Answer: The answers C

Step-by-step explanation: Use Desmos to find it

Answer:

Option C.

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given graph it is clear that the related line passes thorough the points (0,2.5) and (2,-1.5).

The equation of related line is

[tex]y-2.5=\frac{-1.5-2.5}{2-0}(x-0)[/tex]

[tex]y-2.5=\frac{-4}{2}(x)[/tex]

[tex]y-2.5=-2x[/tex]

Add 2.5 on both sides.

[tex]y-2.5+2.5=-2x+2.5[/tex]

[tex]y=-2x+2.5[/tex]

Th sign of inequality is either ≤ or ≥ because the related line is a solid line. It means the points on the line are included in the solution set.

Let the required inequality is

[tex]y\geq -2x+2.5[/tex]

(1,1) is included in the shaded region. So, the above inequality is true for (1,1).

[tex]1\geq -2(1)+2.5[/tex]

[tex]1\geq 0.5[/tex]

The assumed inequality is true for (1,1). So, the required inequality isn [tex]y\geq -2x+2.5[/tex].

Therefore, the correct option is C.

Final answer:

The constant of proportionality for dollars earned per hour worked is 6.25, and the constant of proportionality for hours worked per dollar earned is 0.16.

Explanation:

To find the constant of proportionality for dollars earned per hour worked, we can use the formula y = kx, where y is the amount earned and x is the number of hours worked. Given that Lucy earned $25 for 4 hours of work, we can substitute these values into the equation:

25 = k * 4

Solving for k, we divide 25 by 4:

k = 25 / 4 = 6.25

Therefore, the constant of proportionality for dollars earned per hour worked is 6.25.

To find the constant of proportionality for hours worked per dollar earned, we can rearrange the equation to x = my, where x is the number of hours worked and y is the amount earned. Substituting the values, we get:

4 = m * 25

Solving for m, we divide 4 by 25:

m = 4 / 25 = 0.16

Therefore, the constant of proportionality for hours worked per dollar earned is 0.16.

Final answer:

The perimeter of the rectangle is calculated using the formula P = 2l + 2w, converting the height from millimeters to centimeters and then applying the values to get a perimeter of 70.6 cm.

Explanation:

To calculate the perimeter of a rectangle, we use the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. In this case, the rectangle's length is given as 30 cm, but the height (which can be considered as the width in the context of the perimeter) is given in millimeters. First, we need to convert the height to centimeters by dividing the number of millimeters by 10, because there are 10 millimeters in a centimeter. So, 53 mm is equivalent to 5.3 cm. Now, we apply the formula to find the perimeter:

P = 2 × 30 cm + 2 × 5.3 cm = 60 cm + 10.6 cm = 70.6 cm.

Therefore, the perimeter of the rectangle is 70.6 cm.

Rewrite the fractions with common denominators and then answer:

A:

13/14 > 25/28

26/28 > 25/28    

This is True

B) 21/45 < 20/45  False

C) 10/12 > 11/12

False

D) 20/25 < 8/25

False

The true statement is A.

Answer:

Part a) The estimate amount of medicine is 30.0 grams

Part b) The actual amount of medicine is 29.925 g. The difference between the  estimate and the actual amount, is 0.075 g

Part c) 5.985 grams

Part d) 6 grams

Step-by-step explanation:

The complete question is

Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5  doses of medicine.

a. About how much medicine did he make in grams? Estimate the amount of each chemical by  rounding to the nearest tenth of a gram before finding the sum. Show all your thinking.

b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your  estimate and the actual amount?

c. How many grams are in one dose of medicine? Explain your strategy for solving this problem.

d. Round the weight of one dose to the nearest gram

Part a) round  to the nearest tenth of a gram first

Chemical A

10.357 g -----> 10.4 g

Chemical B

12.062 g -----> 12.1 g

Chemical C

7.506 g -----> 7.5 g

To find out the estimate amount of medicine sum the three values

10.4+12.1+7.1=30.0 g

therefore

The estimate amount of medicine is 30.0 grams

Part b)

The actual amount of medicine is

10.357+12.052+7.506=29.925 g

To find out the difference between your  estimate and the actual amount, subtract the actual amount from the estimate

30.0-29.925=0.075 g

Part c) To find out how many grams are in one dose of medicine, divide the actual amount of medicine by five

29.925 g/5=5.985 g

Part d) Round the weight of one dose to the nearest gram

we have

5.985 g ------> 6 g

Answer:

No Solution

Step-by-step explanation:

-1/7(14+28p)-13=4(1/2p-3)-6p

-2-4p-13=2p-12-6p

rearrange the question so like terms are next to each other

-2-13-4p=2p-6p-12

-15-4p=-4p-12

add 12 to both sides

-3-4p=-4p

add 4p to both sides

-3=0

No solution

Answer:

something is wrong in the equation

Step-by-step explanation:

Answer:

[tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

we know that

Absolute value is a term which is used to indicate the distance of a point or number from the origin of a number line or coordinate system.

In this problem

we have to find the absolute value of the given number

[tex]\left \| -2\frac{2}{3} \right \|[/tex]

that means we have to find the distance of [tex]\left \| -2\frac{2}{3} \right \|[/tex]  from the origin of a number line.

Distance of [tex]-2\frac{2}{3}[/tex] from the origin is [tex]2\frac{2}{3}[/tex] .

Remember that the distance cannot be a negative number.

Therefore, the absolute value of [tex]\left \| -2\frac{2}{3} \right \|[/tex] is [tex]2\frac{2}{3}[/tex]

see the attached figure to better understand the problem

Answer:

2_2/3  

Step-by-step explanation:

Answer:

1.65 X 10^-3 (i don't know if your teacher wants you to also add the unit at the end, but if your teacher does, then just add metric ton at the end. :-) )

Step-by-step explanation:

We want to bring the decimal point to the right of the first number, so you move the decimal point 3 times to the right, which would give you 1.65 metric ton.

So you should know that moving a decimal point to the right would make the power negative, and moving the decimal point to the left would make the power positive.

In this situation, the power would be negative, and a negative three, because you moved the decimal point 3 times to the right.

Hope this helped :-) <3

The slope of this graph is rise over run which means how much your distance x has between the 2 points and how much y increased between those 2 points. So it starts at (1,-2) and ends at (2,1). So x had a run of 1 and y had a rise of 3 we have 3/1 which is equivalent to 3, so the answer would be B.

Answer:

the total amount spent was$2.34 cents

Answer:

He spent $ 2.34 in all.

Step-by-step explanation:

Given,

The amount spent on the bottle of paint = $ 1.89,

While, the amount spent on the brush = $ 0.45,

Hence, the total amount spent = amount spent on paint + amount spent on brush

[tex]= 1.89 + 0.45[/tex]

[tex]= \$ 2.34[/tex]

i.e. Lawrence spent total $ 2.34 in both.

Answer:

6.25 km an hour

please mark brainliest

Step-by-step explanation:

Answer:

Average velocity = 6.25 km/h

Step-by-step explanation:

Given  : A horse began running due east and covered 25 km in 4.0 hr.

To find :  What is the average velocity of the horse.

Solution : We have given

Displacement  = 25 km

Time = 4 hr.

Velocity = [tex]\frac{Total\ displacement}{time}[/tex].

Velocity = [tex]\frac{25}{4}[/tex].

Average velocity = 6.25 km/h

Therefore, Average velocity = 6.25 km/h

Answer:

Step-by-step explanation:

The given expression is

[tex]\frac{x^{3}-1}{x^{3}+x^{2}+x}[/tex]

This expression is rational, which means the denominator must be different to zero, otherwise, the function will be undefined. So, let's find if there are values that make the denominator zero.

[tex]\frac{x^{3}-1}{x^{3}+x^{2}+x}=\frac{x^{3}-1}{x(x^{2}+x+1)}[/tex]

So, if we evaluate the expression with [tex]x=0[/tex], we would have

[tex]\frac{x^{3}-1}{x(x^{2}+x+1)}=\frac{0^{3}-1}{0(0^{2}+0+1)}=\frac{-1}{0}[/tex]

As you can observe, there must be one exclusion, because it makes the expression undefined.

Therefore, the answer is true.

Answer:

4:5

Step-by-step explanation:

You can divide both numbers by 12, therefore simplifying the numbers to the lowest they can be

Answer:

Ratio of table to chair : [tex]\frac{4}{5}[/tex].

Step-by-step explanation:

Given : furniture store sells 48 tables for every 60 chairs in a given week.

To find : what is the unit rate of tables to chairs.

Solution: We have given

Table = 48 .

Chair = 60 .

Ratio of table to chair : [tex]\frac{48}{60}[/tex].

On dividing both number by 4

Ratio of table to chair : [tex]\frac{12}{15}[/tex].

On dividing both number by 3

Ratio of table to chair : [tex]\frac{4}{5}[/tex].

Therefore, Ratio of table to chair : [tex]\frac{4}{5}[/tex].

Answer:

4.9 x 10^-4 is the scientific notation

Move the decimal 4 places from left to right

Answer:

[tex]\displaystyle 4,9 \times 10^{-4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 0,00049 = 4,9 \times 10^{-4}[/tex]

You move the decimal mark four times to the left.

I am joyous to assist you anytime.

Triangle MNO was dilated (increased) and then rotated to create triangle YHO.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure to create an image.

Triangle MNO was dilated (increased) and then rotated to create triangle YHO.

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Answer:

x = 90

c = 11

d = 11

Step-by-step explanation:

For this, we just need to use algebra to solve for x.

(x / 3) - 4 = 26 | First we add 4 to both sides

x / 3 = 30 | Then we multiply both sides by 3

x = 90.

For the others, it's the same.

-8 + 10c = 102 | Subtract -8 from both sides, or add 8

10c = 110 | Divide both sides by 10

c = 11

2.5d + 7.5 = 20 | Subtract 7.5 from both sides

2.5d = 27.5 | Divide both sides by 2.5

d = 11

To achieve an overall interest of 10.6% on her $3,000 investment, Hattie should put $900 into an account with a 12% interest rate and $2,100 into an account with a 10% interest rate.

Let's denote the amount of money Hattie puts in the 12% interest account as x, and the amount she puts in the 10% interest account as 3000 - x. Her aim is that the total interest she earns from both accounts is 10.6% of her total investment ($3,000).

So, 0.12x (interest from the first account) + 0.10(3000-x) (interest from the second account) should equal 0.106*3000 (her total desired income).

By solving this equation we can determine the amount of money Hattie should place in each account:

So, Hattie should put $900 in the 12% account and the rest, which is $2,100, in the 10% account to get her goal of 10.6% total interest.

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To solve this problem, set up a system of equations using the amount of money Hattie puts into each account and the total interest earned. Solve the system to find the values of x and y.

To solve this problem, we can set up a system of equations. Let's call the amount of money Hattie puts into the account that earns 12% per year x, and the amount of money she puts into the account that earns 10% per year y. We know that x + y = $3,000 (since she has $3,000 to invest). We also know that the total interest earned is equal to 10.6% of $3,000, which is 0.106 * $3,000 = $318.

The interest earned from the account that earns 12% per year is 0.12x, and the interest earned from the account that earns 10% per year is 0.1y. We can set up another equation based on this: 0.12x + 0.1y = $318.

Now we have a system of equations: x + y = $3,000 and 0.12x + 0.1y = $318. We can solve this system using substitution or elimination to find the values of x and y.

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Answer:

Step-by-step explanation:

(a) Answer below

[tex]v = u + at[/tex]

[tex](10) = u + (2)(3)[/tex]

[tex]10 = u + 6[/tex]

[tex]u = 4[/tex]

(b) Answer below

[tex]v = u + at[/tex]

[tex](29) = (5) + (4)t[/tex]

[tex]29 = 5 + 4t[/tex]

[tex]24 = 4t[/tex]

[tex]t = 6[/tex]

[tex]\text{Hello there!}\\\\\text{Plug in and solve:}\\\\1. \\\\10=u+2(3)\\\\10=u+6\\\\\boxed{4=u}\\\\2.\\\\29=5+4(t)\\\\24=4(t)\\\\\text{Divide by 4}\\\\\boxed{6=t}[/tex]

Answer:

10/7

Step-by-step explanation:

Step 1: Subtract 12x from both sides.

−2x+5−12x=12x−15−12x

−14x+5=−15

Step 2: Subtract 5 from both sides.

−14x+5−5=−15−5

−14x=−20

Step 3: Divide both sides by -14.

−14x/14=−20/14

x=10/7

You get 10 over 7 because you simplify 20 over 14 by dividing them by 2 which would give you 10/7.