find the value of each variable or indicated measures​

Answer:

10x - 13

Step-by-step explanation:

1/2 (8x - 2) + 3/4 (8x - 16) Distribute the fractions. ->

(to distribute multiply the number outside the parentheses to each one inside the parentheses. Ex: 1/2 x 8 = 4 so its 4x for the first one, then do that same for 1/2 and -2)

4x - 1 + 6x - 12 Add like terms. ->

(Add the like terms are numbers/variables that are similar. Ex: 4x and 6x, add them together and you get 10x then do the same for -1 and -12)

10x - 13 <- The Answer

Answer:

5/14

Step-by-step explanation:

Answer:

Gina has 5 large shipping boxes and 6 small shipping boxes.

Step-by-step explanation:

32 items to ship and 11 shipping boxes.

Large=4 items

4 X 5 = 20

Small=2 items

2 X 6 = 12

20 + 12 = 32

Answer:

Starting with:

-15 > -11 + w

Add 11 to both sides:

-15 + 11 > w

Simplifying:

-4 > w

Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:

w < -4

Answer:

18 fourths

Step-by-step explanation:

4.5 x 4=18

or

each apple would produce 4 fourths so 4 apples would produce 16. Then 1/2 apple would produce 2 fourths so 16 + 2 = 18

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:x=5

Step-by-step explanation:

2x-4=6 Then you at 4 to both sides

2x=10 Divide

x=5

The number of grapes that 8 people eat more than 5 people, given the table attached, is 34 kg of grapes

To find the amount of grapes that 8 people eat more than 5 people, the formula would involve subtracting the amount of grapes eaten by 5 people from the amount of grapes eaten by 8 people.

From the graph, the amount of grapes eaten by 8 people would be 74 kg of grapes. The amount of grapes eaten by 5 people was 40 kg of grapes.

The amount of grapes that 8 people eat more than 5 people, is therefore :

= Grapes eaten by 8 people - Grapes eaten by 5 people

= 74 - 40

= 34 kg of grapes

In conclusion, the amount of grapes that 8 people eat more than 5 people, is 34 kg of grapes.

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Answer: 5 11/12 not sure

Answer:-1.38

19/50=.38 in decimal form +(-1) = -1.38

Answer:

uytrfvvhhhhhhhjkklñññññlluuyjnkuyjuyjju

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

$0.90

Step-by-step explanation:

Answer:

$0.90

Step-by-step explanation:

Assuming there are no taxes or additional costs, one simply has to divide the total cost by the amount purchased to find the unit price, hence;

2.7 / 3

= 0.9

1. Using a calculator, we find that cos 10 ≈ 0.98.

2. Using a calculator, we find that sin 30 ≈ 0.50.

3. Using a calculator, we find that sin 20 ≈ 0.34.

4. Using a calculator, we find that tan 25 ≈ 0.47.

5. Using a calculator, we find that tan 48.5 ≈ 1.14.

Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:

Cos 10:

Using a calculator, we find that cos 10 ≈ 0.98.

Sin 30:

Using a calculator, we find that sin 30 ≈ 0.50.

Sin 20:

Using a calculator, we find that sin 20 ≈ 0.34.

Tan 25:

Using a calculator, we find that tan 25 ≈ 0.47.

Tan 48.5:

Using a calculator, we find that tan 48.5 ≈ 1.14.

These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.

Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.

It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.

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There will be 319 boards be required

and the total cost be $223,720.

Given, a classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m.

Now, we have to find the number of boards needed altogether

So, the area of the ceiling is

Area = 6.8×4.7

Area = 319.6 m²

Now, the area of the board is

Area = 1 m²

So, 319 boards will be required to cover the ceiling.

Now, if one board costs $700 then,

the total cost be

= 700×319.6

= $223,720

Hence, There will be 319 boards be required

and the total cost be $223,720.

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Answer:

(0, 2)

Step-by-step explanation:

Answer:

\(\text{$y$-intercept$\;=\log_2 \left(\dfrac{27}{64}\right) \approx -1.245$}\)

Step-by-step explanation:

The y-intercept is the value of y when x = 0.

Therefore, to find the y-intercept of y = 3 log₂(x + 3) - 6, substitute x = 0 into the equation and solve for y.

\(\implies y=3 \log_2(0+3)-6\)

\(\implies y=3 \log_2(3)-6\)

Using the log law logₐ(a) = 1, rewrite 6 with log base 2:

\(\implies y=3 \log_2(3)-6\log_2(2)\)

\(\textsf{Apply the log power law:} \quad n\log_ax=\log_ax^n\)

\(\implies y=\log_2(3)^3-\log_2(2)^6\)

\(\implies y=\log_2(27)-\log_2(64)\)

\(\textsf{Apply the log quotient law:} \quad \log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)\)

\(\implies y=\log_2 \left(\dfrac{27}{64}\right)\)

Therefore, the exact value of the y-intercept of the given equation is log₂(27/64) which is approximately -1.245 to the nearest thousandth.

Answer:

1296°F

Step-by-step explanation:

950+346=1296

Hope this helps! : )

Using proportions, the amount of horizontal change in your position is of 180 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The horizontal change is of 9% for each feet descended, hence, for 2000 feet descended, the horizontal change is given by:

0.09 x 2000 = 180 feet.

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Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

the answer is (b.)41.7cm²

the workings;;

9.2cm×4cm+5cm=41.8 or 41.7cm²

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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Answer:

Step-by-step explanation:

This equation represents the relationship between the exponential functions y = e^x and y = (10^(x-1)). These two functions are equal to each other for all values of x. This can be shown by taking the natural logarithm of both sides of the equation, which gives us:

ln(e^x) = x-1

In this equation, ln(e^x) is equal to x, since the natural logarithm of an exponential expression with a base of e is the exponent. Therefore, we can simplify the equation by taking the natural logarithm of both sides:

ln(10^(x-1)) = x-1

e^(x-1) = 10^x

The two functions e^x and 10^(x-1) are the same function with different bases, so they follow the same pattern. The fact that these two functions are equal to each other for all values of x can also be shown by graphing the two functions and seeing that they overlap perfectly.

Telling Marvin the number 18 should get us into the museum.

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse of multiplication, and is used to find out how many times one number is contained within another number.

To get into Marvin's Magic Museum, we need to figure out which number Marvin likes based on the given information.

Marvin likes the number 14, but not 15. This suggests that he likes even numbers, since 14 is even and 15 is odd.

Marvin likes the number 21, but not 26. This suggests that he likes numbers that are divisible by 3, since 21 is divisible by 3 and 26 is not.

Marvin likes the number 35, but not 39. This suggests that he likes numbers that are not divisible by 4, since 35 is not divisible by 4 and 39 is.

Putting these clues together, we can see that the number Marvin likes must be even, divisible by 3, and not divisible by 4. The only number in the list that meets these criteria is 18, since it is even, divisible by 3 (6 times), and not divisible by 4.

Therefore, telling Marvin the number 18 should get us into the museum.

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Answer:

\(\cos\theta = \pm\frac{2\sqrt{2}}{3}\\\tan\theta=\pm\frac{\sqrt{2}}{4}\)

Step-by-step explanation:

sinθ = 1/3

\(\cos\theta=\pm\sqrt{1-\cos^2\theta} = \pm\sqrt{1-\frac{1}{9}}=\pm\sqrt\frac{8}{9}=\pm\frac{2\sqrt{2}}{3}\)

\(\tan\theta=\frac{\sin\theta}{\cos\theta}=\pm\frac{1}{2 \sqrt{2}}=\pm\frac{\sqrt{2}}{4}\)

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

To determine which set of side measurements could form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side. This is known as the Triangle Inequality Theorem.

Let's check each set of side measurements:

13, 19, 7:

The sum of the two shorter sides is 7 + 13 = 20, which is greater than the longest side (19). Therefore, this set of side measurements could form a triangle.

25, 12, 13:

The sum of the two shorter sides is 12 + 13 = 25, which is equal to the longest side (25). Therefore, this set of side measurements could form a triangle.

18, 2, 24:

The sum of the two shorter sides is 2 + 18 = 20, which is greater than the longest side (24). Therefore, this set of side measurements could form a triangle.

3, 1, 5:

The sum of the two shorter sides is 1 + 3 = 4, which is less than the longest side (5). Therefore, this set of side measurements could not form a triangle.

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

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Answer:

yes

no

yes

no

hope this helps

Answer:

1. Yes

2. No

3.Yes

4.No

Step-by-step explanation:

I did the test and got it right!

The numeric value of f(x) = 3x² - 7x - 4 at x = 0 is given as follows:

f(0) = -4.

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² - 7x - 4

We want to find the numeric value of the function at x = 0, hence both instances of x in the definition of the function are replaced by zero and then we add the terms, as follows:

f(0) = 3(0)² - 7(0) - 4

f(0) = -4.

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9514 1404 393

Answer:

  2π

Step-by-step explanation:

The first peak is shown at x=π/2. The next peak is shown at x=5π/2. The difference in x-values between repeating parts of the graph is ...

  5π/2 -π/2 = 4π/2 = 2π

The period of the function shown is 2π.