One number is three less than five times another. If their sum is decreased by four, the result is twenty-three. Find the numbers.

Answer:

5

Step-by-step explanation:

Hop the spaces from 1 until you reach to 6 and you get 5 hops

Answer:

2

Step-by-step explanation:

( \(\frac{1}{2}\) × 4 ) × 5 - 2³ = 10 - 8 = 2

Answer:

I think AC is 6.

Step-by-step explanation:

This looks like an equilateral triangle so that means because there is a 3 on  one side of the line it should be the same on the other side of the line so 3 x 2 = 6.

Step-by-step explanation:

\(triangle \: abd \\ using \: pythagoras \: theorem \\ {hyp}^{2} = {adj}^{2} + {opp}^{2} \\ {12}^{2} = {3}^{2} + {opp}^{2} \\ 144 = 9 + {x}^{2} \\ 144 - 9 = {x}^{2} \\ 135 = {x}^{2} \\ take \: the \: square \: of \: both \: sides \\x = 11.62\)

using the opposite side of triangle and

\(using \: pythagoras \: theorem \\ {16}^{2} = {11.62}^{2} + {x}^{2} \\ 256 = 135.02 + {x}^{2} \\ 256 - 135.02 = {x}^{2} \\ 120.198 = {x}^{2} \\ take \: the \: roots \: of \: both \: sides \\ x = 10.96\)

therefore the length of line AC

\( = 3 + 10.96 \\ = 13.96\)

hope this helps

Given:

Seema deposited $800 in a saving account earning 3.24% compounded

annually.

So, we can conclude the following data:

P = initial investement = 800

r = interest ratio = 3.24% = 0.0324

n = 1

t = time 3 years

The final investment (A) will be calculated using the following formula:

Substitute with the given data:

Rounding to the nearest cent

So, the answer will be $880.31

Answer:

Step-by-step explanation:

\(y=(\frac{1}{g} )x\)

Constant up a proportionally is  \(\frac{1}{g}\).

Solution:

Given:

Circumference = 56.52m

We are required to determine the radius

Answer:

Radius = 9mi

Step-by-step explanation:

Radius = 9mi

R = D/2

R = 18/2

R= 9mi

Answer:

1/6

Step-by-step explanation:

1/2÷3

1/2×1/3

1×1/2×3

1/2×3

1/6

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Surface S = √21

A surface integral in mathematics is a generalization of multiple integrals to integration over surfaces, particularly in multivariable calculus. It can be viewed as the line integral's double integral equivalent. One can integrate a vector field or a scalar field across a given surface.

Equation of surface (S) is,

x/1 - y/2 + z/4 = 1

From here we get,

z = 4 - 4x + 2y

∫∫(S)xdS = ∫∫ (D)x(1 + (∂z/∂x)² + (∂z/∂y)²)^1/2 dxdy

Here (D) is projection of (S) on xy coordinate plane

so, (D) is triangle with vertices (1, 0, 0), (0, - 2, 0) and  (0,0,0).

∂z/∂x = - 4, ∂z/∂y = 2.

In (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0.

Now we have,

∫∫(S)xdS = ∫∫(D)x(1 + (- 4)² + 2²)^1/2 dxdy

= √21∫₋₂⁰dy ∫₀¹xdx

= √21y₋₂⁰x²/2₀¹

= √21

Hence, Domain of integration is (D) 0 ≤ x ≤ 1, - 2 ≤ y ≤ 0 and Surface S = √21

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The inverse of the point can be gotten by exchanging the coordinates of the ordered pair. Therefore

The point on the graph is

Answer:

y + 4x

Step-by-step explanation:

For this problem, we will simply combine like terms using the distributive property and the commutative property.

First, let's use the commutative property:

2y + x + 3x - y

= 2y - y + x + 3x

Second, let's use the distributive property:

2y - y + x + 3x

= y ( 2 - 1 ) + x ( 1 + 3 )

= y ( 1 ) + x ( 4 )

= y + 4x

Hence, the simplification of 2y + x + 3x - y is y + 4x.

Cheers.

The measure of the angle ABC given that the bisector is ABP is 12n degrees

From the question, we have the following parameters that can be used in our computation:

Angle measures

The angle measures and the relationships are given as

Using the above as a guide, we have the following:

The above statements mean that

ABC = 2 * ABP

substitute the known values in the above equation, so, we have the following representation

ABC = 2 * 6n

Evaluate the products

ABC = 12n

Hence, the measure is 12n degrees

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Step-by-step explanation:

\( = 3 {a}^{3} {b}^{2} c + 9a {b}^{2} {c}^{3} \)

\( = (3a {b}^{2} c)( {a}^{2} ) +( 3a {b}^{2} c)(3 {c}^{2} )\)

\( = 3a {b}^{2} c( {a}^{2} +3 {c}^{2} )\)

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

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

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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Answer:

y= 11. 125

Step-by-step explanation:

8 y = 89

because you do not have another y on the other side simple divide

8 y = 89

89 / 8 = y

y= 11. 125

(Not sure what decimal place to round to  so there are all 3 )

Hey there!

8y = 89

DIVIDE 8 to BOTH SIDES

8y/8 = 89/8

SIMPLIFY IT!
y = 89/8

y ≈ 11 1/8

y ≈ 11.125

Therefore, the answer is:

y = 89/8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

5/4

Step-by-step explanation:

Answer:

exact form 5/4

1 1/2 for a mixed number

1.25 as a decimal

9514 1404 393

Answer:

  x = 1/6

Step-by-step explanation:

The relevant rules of exponents are ...

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

__

The fraction inside parentheses evaluates to ...

  3^(3/4 -3/8) = 3^(3/8)

Then the whole expression evaluates to ...

  (3^(3/8))^(4/9) = 3^((3/8)(4/9)) = 3^(12/72) = 3^(1/6)

The value of x is 1/6.

C = F - 32

F = C + 32

9514 1404 393

Answer:

  351.48 cm²

Step-by-step explanation:

Heron's formula can be used to find the area from three side lengths.

  A = √(s(s -a)(s -b)(s -c)) . . . . where s=(a+b+c)/2

  s = (30 +30 +26)/2 = 43

  A = √(43(43-30)(43-30)(43-26)) = √(43(13)(13)(17)) = √123,539

  A ≈ 351.48 . . . square centimeters

The correct answer is (c) sec^2α.

What is the Pythagorean theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The expression tan^2α + 1/secα can be simplified using trigonometric identities. Recall the following trigonometric identities:

tan^2α + 1 = sec^2α (Pythagorean identity for tangent)

secα = 1/cosα (definition of secant)

Substituting these identities into the original expression, we get:

tan^2α + 1/secα = sec^2α + 1/secα

Now, we can combine the terms with a common denominator:

(sec^2α * secα + 1)/secα

Using the definition of secant (secα = 1/cosα), we can further simplify:

(1/cos^2α * 1/cosα + 1)/secα

Multiplying numerator and denominator by cos^3α, we get:

(1 + cosα)/secα

Recalling that secα = 1/cosα, we can replace secα with its definition:

(1 + cosα)/(1/cosα)

Finally, multiplying the numerator and denominator by cosα, we get:

cosα + 1/cosα

Hence, the equivalent expression for tan^2α + 1/secα is cosα + 1/cosα, which is equivalent to sec^2α for all values of α for which secα is defined. Therefore, the correct answer is (c) sec^2α.

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The canister holds 80 cups and they need 84 cups of flour to make a dozen pizzas. So, the cooks cannot make a dozen pizzas without refilling the canister. The solution has been obtained by using unitary method.

What is the unitary method?

The unitary technique is used to first calculate the value of each individual unit, and only then is the value of the necessary quantity of units calculated.

We are given that a pizzeria stores flour in a 5-gallon container. We assumed that 16 cups make 1 gallon.

So, number of cups that will make 5 gallon is 16 * 5 = 80 cups

Since, each pizza they make uses 7 cups of flour. So, for making 12 pizzas, they require 12 * 7 = 84 cups of flour.

Hence, the cooks cannot make a dozen pizzas without refilling the canister.

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Answer:

f(x) = 19

Step-by-step explanation:

f(x) = 2x2 + 1

f(x) = 2(3)2 + 1

f(x) = 2(9) + 1

f(x) = 18 + 1

f(x) = 19

Follow PEMDAS from left to right

P.E.M.D.A.S:

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

Answer:

To solve this problem, we need to use the Poisson distribution, which describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence.

Let λ be the average number of calls per minute. From the problem statement, we have λ = 2.35.

Now we need to find the probability of having at most 2 phone calls in one minute. Let X be the random variable representing the number of phone calls in one minute. Then we have:

P(X ≤ 2) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!) + e^(-λ) * (λ^2/2!)

Substituting λ = 2.35, we get:

P(X ≤ 2) = e^(-2.35) * (2.35^0/0!) + e^(-2.35) * (2.35^1/1!) + e^(-2.35) * (2.35^2/2!)

≈ 0.422

Therefore, the probability that during one particular minute there will be at most 2 phone calls is about 0.422, or 42.2%.

Answer:

B. They are not parallel because their slopes are not equal.

Step-by-step explanation:

Find the slope of the line that runs through points (6, 3) and (-1, 5):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} \)

\( slope (m) = \frac{2}{-7} = -\frac{2}{7} \)

Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.

The answer is "B. They are not parallel because their slopes are not equal."

Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)

The range of all possible values of $x$

I. (x + 15) + (2x + 15) > 4x + 15 —-> 3x + 30 > 4x + 15 —-> 15 > x ---> x < 15

II. (x + 15) + (4x + 15) > 2x + 15 —-> 5x + 30 > 2x + 15 —-> 3x > -15 ---> x > -5

III. x + 15 + (2x + 15) + (4x + 15) — 6x + 30 > x + 15 —-> 5x > -15 ---> x > -3

Since the sum of any two sides of a triangle must be bigger than the sum of its third side, if you are only examining all real numbers as potential replacements for x in the triangle whose sides are x + 15, 2x + 15, and 4x + 15, then there are these three possibilities:

I. (x + 15) + (2x + 15) > 4x + 15 —-> 3x + 30 > 4x + 15 —-> 15 > x ---> x < 15

II. (x + 15) + (4x + 15) > 2x + 15 —-> 5x + 30 > 2x + 15 —-> 3x > -15 ---> x > -5

III. x + 15 + (2x + 15) + (4x + 15) — 6x + 30 > x + 15 —-> 5x > -15 ---> x > -3

The solution is (-3, 15). If you substitute a number of -4 or -5 for x, one of the triangle's sides will be negative.

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