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2 years ago

Find the measure of arc FD

Mathematics

1 answer:

Mekhanik [1.2K]2 years ago

3 0

Answer: 49 degrees

Step-by-step explanation:

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(-2/3)^7*(3/5)^6*(5/6)^5*(1/3)^-7 simplify of law of indices

Wewaii [24]

Answer:

$\boxed {-\frac{12}{5}}$

Step-by-step explanation:

Solve the following expression:

$(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $-\frac{2}{3}$ to the power of $7$ :

$(-\frac{2}{3})^{7} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{3}{5}$ to the power of $6$ :

$-\frac{128}{2187} \times (\frac{3}{5})^{6} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Multiply both $-\frac{128}{2187}$ and $\frac{729}{15625}$ :

$-\frac{128}{2187} \times (\frac{729}{15625}) \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{5}{6}$ to the power of $5$ :

$-\frac{128}{46875} \times (\frac{5}{6})^{5} \times (\frac{1}{3})^{-7}$

$-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}$

-Multiply both $-\frac{128}{46875}$ and $\frac{3125}{7776}$ :

$-\frac{128}{46875} \times (\frac{3125}{7776}) \times (\frac{1}{3})^{-7}$

$-\frac{4}{3645} \times (\frac{1}{3})^{-7}$

-Calculate $\frac{1}{3}$ to the power of $-7$ :

$-\frac{4}{3645} \times (\frac{1}{3})^{-7}$

$-\frac{4}{3645} \times 2181$

-Multiply both the $-\frac{4}{3645}$ and $2187$ :

$-\frac{4}{3645} \times 2181$

$\boxed {-\frac{12}{5}}$

Therefore, the final answer is $-\frac{12}{5}$ .

3 0

3 years ago

Ben's dad is making a large pot of pasta sauce that calls for 3.5 kilograms of tomatoes. If he triples the amount of tomatoes fo

maria [59]

Answer: 10,500 gm

Step-by-step explanation:

Given

Pasta requires 3.5 kg of tomatoes

we know, $1\ kg=1000\ mL$

If the amount is triples, the quantity of tomatoes is $3\times 3.5=10.5\ kg$

$\Rightarrow 10.5\ kg\equiv 10.5\times 1000=10,500\ gm$

Thus, he uses 10,500 gm of tomatoes

7 0

2 years ago

20 points! Identify the solids that form the compos

Troyanec [42]

The composite shape is made up of a cube with a side length of 5 inches and a cylinder with a radius of 2 inches and a height of 4 inches.

The composite solid's surface area is 225.4 square inches.

Step-by-step explanation:

Step 1:

The given composite shape is made up of a cube with a side length of 5 inches and a cylinder with a radius of 2 inches and a height of 4 inches.

The surface area of the composite shape is given by summing the individual surface areas.

The composite shape's surface area = The cube's surface area + the cylinder's surface area.

Step 2:

Any cube's surface area is calculated by multiplying 6 with the square of the side length ( $a^2$ ).

The cube's surface area = $6a^2$ = $6(5^{2} )$ = $150$ square inches.

Step 3:

Any cylinder's surface area is calculated with the following formula;

The cylinder's surface area = $2 \pi r h+2 \pi r^{2}$ = $2 \pi (2) (4)+2 \pi (2)^{2}$ = $75.398$ square inches

Step 4:

The composite shape's surface area = The cube's surface area + the cylinder's surface area.

The composite shape's surface area = 150 + 75.398 = 225.398 square inches. Rounding this off, we get the area as 225.4 square inches.

3 0

3 years ago

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It

Nezavi [6.7K]

Answer:

There is no sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

We are given;

n = 27 bags

Sample mean;X = 402 gram

Population mean;μ = 404 gram

Variance = 676

We know that, standard deviation(σ) = √variance

Thus;

σ = √676

σ = 26

The hypotheses are;

Null hypothesis; H0: μ = 404

Alternative hypothesis; HA: μ < 404

Let's find the z-score from the formula;

z = (X - μ)/(√σ/n)

z = (402 - 404)/√(26/27)

z = -2.04

From the z-distribution table attached, we have a p-value of 0.02068

This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled

6 0

4 years ago

What is the angle that forms from the two vectors below? *<br> v= <-12,5>, w= <3,-10>

Vera_Pavlovna [14]

Answer:

Step-by-step explanation:

3 0

2 years ago