Which expression represents this word phrase?

The product of 3 &4

A. 3 × 4
B. 3 +4
C. 3/4
D. 7 - 4 ​

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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Although part of your question is missing, you might be referring to this full question: Which of the following options is an equivalent function to f(x) = 2(5)^2x? choices:

f(x) = 50^x

f(x) = 100^x

f(x) = 2(25)^x

f(x) = 4(25)^x

The equivalent function too expression is f(x)= 2(25)ˣ. Thus option c is correct.

The expression of function f(x) given, f(x)=2(5)²ˣ.

Functions are said to be equal if they have same domain or codomain such that f(x) = g(x). Thus, the two functions are equal functions.  

∴ The function after solving expression is,

f(x)= 2×(5²)ˣ

f(x)= 2×(25)ˣ

Hence, the correct equivalent function is f(x)= 2(25)ˣ.

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Answer:

The function would be odd

The answer is neither.

Let's take an odd number and substitute.

Now, let's take an even number.

Since both even and odd numbers are possible, it is neither.

Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

Answer:

∠ T = 46°

Step-by-step explanation:

the secant- secant angle T is half the difference of the measures of the intercepted arcs , that is

∠ T = \(\frac{1}{2}\) (DR - ML) = \(\frac{1}{2}\) (136 - 44)° = \(\frac{1}{2}\) × 92° = 46°

Answer:

h = b - a

Step-by-step explanation:

Answer:

A/b = h

Step-by-step explanation:

A=bh

1) divide both sides by b

A/b = h

Answer:

D) F

Step-by-step explanation:

The ratio given is 1 : 6

The equivalent is 7 : x

To calculate x;

The number that makes the ratio equivalent is therefore 42

The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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Answer:

D, and C sorry if I'm wrong

this contain two triangle and one rectangle

therefore total area = 2×area of triangle + area of rectangle

then refer the attachment

Answer:

option d

Step-by-step explanation:

option d because the vertical asymptotes are -3 and 2, so x cannot be 3 or -2

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

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

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

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

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

The objective function z=f(x, y) that represents the total cost for spaying x female cats and neutering y male cats is f(x, y) = 83x + 49y

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

Represent the female cat with x and the male cat with y

So, we have the following equation

Total amount = 83x + 49y

Express as a function

z = 83x + 49y

Hence, the objective function is z = 83x + 49y

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The number of revolutions made by the wheel is 5.24 ≅ 5.  

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.    

Here we have

A wheel rotated by 1888°  

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°  

Let the wheel make 'x' revolution to make 1888°  

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.    

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Answer:

y = 0.2 * exp ((3/2) x ^ 2)

Domain: all real numbers

Step-by-step explanation:

Answer: The constant of proportionality is r = 5.

Step-by-step explanation:

O, we know that x and y are proportional, this means that:

y = r*x

where r is the constant of proportionality.

we also have the table

x    y

7    35

12   60

20   100

Now, we can replace those values in our equation and get, for the first pair:

35 = r*7

r = 35/7 = 5

for the second pair:

60 = r*12

60/12 = 5 = r

So we can conclude that the constant of proportionality is 5.

Answer:

5

Step-by-step explanation:

It was right for me on khan

Answer:

-9/14 so the answer is B

Step-by-step explanation:

Hope this helps!!!!

Answer:

the answer is b

Step-by-step explanation:

Answer:

x = -14

Step-by-step explanation:

(x+1)² + 120 = (x-3)²

expand each binomial:

x² + 2x + 1 + 120 = x² -6x + 9

combine 'like terms' to simplify:

8x = -112

x = -14

Answer:

as i see

the answer is 32.....

Given:

The vertices of the triangle are (-10,-3), (1,4) and (-1,7).

To find:

The perimeter of the triangle.

Solution:

Distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let the vertices of the triangle are A(-10,-3), B(1,4) and C(-1,7).

Using distance formula, we get

\(AB=\sqrt{(1-(-10))^2+(4-(-3))^2}\)

\(AB=\sqrt{(1+10)^2+(4+3)^2}\)

\(AB=\sqrt{(11)^2+(7)^2}\)

\(AB=\sqrt{121+49}\)

\(AB=\sqrt{170}\)

Similarly,

\(BC=\sqrt{\left(-1-1\right)^2+\left(7-4\right)^2}=\sqrt{13}\)

\(AC=\sqrt{\left(-1-\left(-10\right)\right)^2+\left(7-\left(-3\right)\right)^2} =\sqrt{181}\)

Now, the perimeter of the triangle is

\(Perimeter=AB+BC+AC\)

\(Perimeter=\sqrt{170}+\sqrt{13}+\sqrt{181}\)

\(Perimeter\approx 13.038+3.606+13.454\)

\(Perimeter=30.098\)

Therefore, the perimeter of the triangle is 30.098 units.

A)  the domain is:

D: [0, 6]

The range is:

B)  

"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."

"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."

And the graph can be seen at the end.

Here we have the linear equation:

d(t) = (1/2)*t + 2

This refers to the amount of water in a barrel for six rainy days, where t is the number of days.

So the domain goes between t = 0 and t = 6.

The range will go between:

d(0) = (1/2)*0 + 2 = 2

d(6) = (1/2)*6 + 2 = 3 + 2 = 5

So the domain is:

D: [0, 6]

The range is:

T: [2, 5]

b) The complete sentences are:

"The slope is __1/2__ So, the water amount in the rain barrel changes at a rate of __1/2__ inch per day."

"The Y-intercept is __2__ So, the amount of water in the rain barrel before the rain began was __2__ inches."

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The archeologist took this measurement to know the value of distance AB

AB=9.610m

Generally, the equation for is  mathematically given as

measure of <ACB=180-(48+81)

                             =180-(129)

                             f <ACB=51

Using sin law in \(\triangle ABC\), we have

\(\frac{sin 51}{100}=\frac{sin 48}{AB}\)

\(AB=\frac{100*sin 48}{sin 51}\)

AB=100*0.74/0.77

AB=9.610m

In conclusion, the length of AB

AB=9.610m

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The vertical line (x = 2) of the vertical line that intersects the graph at the points (2, -2), and (2, 3), indicates that we get;

A function is a relationship that maps the elements from a set A to a set B, such that each element of the set A is mapped to exactly one element of the set B.

The graph in the question indicates a relation in which the value of x has two values of y at points (2, -2), and (2, 3)

Therefore, at x = 2, y = -2, and 3

The vertical line test is used to test if a relation is a function by drawing a vertical line at a value of x and checking if the vertical line intersects the function at more than one point.

If the function intersects the graph at more than one point, then the relationship is not a function

If the function intersects the curve at only one point, then the test indicates that the relationship is a function.

The relationship is not a function, because the vertical line, x = 2 intersects the graph at two points, (2, -2), and (2, 3)

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The amount Aman paid to clear the debt, at last, was Rs. 25,773, including compounded interest of Rs.10,773.

Compound interest is a type of interest system in that accumulated interest attracts interest.

With compounding, interest is paid on interest, unlike the simple interest system.

To compute compound interest, we use the following formula: CI = P( 1 + r/100)^n - P, where CI is compound interest, P is the principal, r is the compound interest rate and n is the number of years.

The amount of the loan = Rs.30,000

Loan period = 4 years

Annual percentage rate = 10%

Compounding period = Annual

Amount after two years = P( 1 + r/100)^n

= Rs. 30,000 x (1 + 0.1)^2

Rs. 36,300 (Rs. 30,000 x 1.21)

Payment after two years = Rs.15,000 (Rs. 30,000 x 50%)

Balance = Rs. 21,300 (Rs. 36,300 - Rs. 15,000)

Amount after another two years = Rs. 21,300 x (1 + 0.1)^2

= Rs. 25,773 ($21,300 x 1.21)

Total payments = Rs. 40,773 (Rs. 25,773 + Rs. 15,000)

Compounded interest = Rs. 10,773 (Rs. 40,773 - Rs. 30,000)

Thus, to settle the loan, lastly, Aman paid Rs. 21,300.

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