what is the expanded notation of -6⁷​

Answer:

61

Step-by-step explanation:

triangles add up to 180

56+63 is 119

180-119 to find the missing angle is 61

hope this helped

Answer:

$77

Step-by-step explanation:

10% of 70$ is $7

$70+$7=$77

Answer:

2 Gallons of Soda

Step-by-step explanation:

that is the answer above

Answer:

140 feet

Step-by-step explanation:

3 seconds times 20 = 1 minute

so you have to do 7 feet times 20 to get 140

Answer:

The area of the shaded region is 36.

Step-by-step explanation:

First, let's find the area of the rectangle as a whole, which will be 5*10 = 50. How did we get 50? The right side is 5 (from 2+3), and the top is 10 (3+7). Multiplying those numbers together will give you the area.

Now, the problem asks to find the shaded region. Let's solve for the area of the non-shaded region: (7*2) = 14.

Now, we can subtract the whole rectangle area minus the non-shaded region to find the shaded region:

50 - 14 = 36

The area of the triangle FGH is equal to  13√10 unit²

Given that the vertices;

F(-5,-7), G(-2,-5), and H(-6,-2)

We have to find the area of the triangle as;

Area of triangle = 1/2bh²

Here,

Area of triangle FGH = 1/2 (GH) (FG)²

Now,

Length of FG =  √26

Length of GH =  √10

Then,

Area of triangle FGH = 1/2 (GH) (FG)²

Area of triangle = 1/2 × √10 × √26²

Area of triangle = 1/2 × √10 × 26

Area of triangle FGH = 13√10

Therefore,

The area of the triangle FGH = 13√10 unit²

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Answer:

D is the answer exponent should be added

hope it helped and stay safe:):):)

\(\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} ~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log\left( \cfrac{x^2}{y^4} \right)\implies \log(x^2)-\log(y^4)\implies 2\log(x)-4\log(y)\)

Answer:

Step-by-step explanation:

A range

Answer:

Step-by-step explanation:

The length of the arc is proportional to the central angle.

The circumference of the circle is given by ...

  C = 2πr

  C = 2π(8 in) = 16π in ≈ 50.265 in

The 60° arc represents 60°/360° = 1/6 of the circle, so its measure will be 1/6 of the total circumference.

 short arc = (1/6)(16π in) ≈ 8.38 in

The remaining portion of the circle is 5/6 of the total circumference, so is ...

  long arc = (5/6)(16π in) ≈ 41.89 in

__

Additional comment

If you use 3.14 for pi, you will get shorter lengths for the arcs. Here, we used the calculator's "pi button."

Answer: hello there here are your answers:

5.d associate property of addition

6.b multiplicative identify

7. c Additive identify

Step-by-step explanation:

5) they are just changing up the number in the ()

6) Its the same number or equation on both sides just wrote different

7) that in a given mathematical system leaves unchanged any element to which it is added.

hope this help have a good day bye!

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:

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

Let's use the variable x to represent the first interest, so the second will be represented by x + 0.04.

Since both interests added are equal to $104, we can write the following equation:

So the first interest is 2% and the second one is 6%.

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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Answer:

4:14

multiply or divide both quantities by the same number

The investment with compound interest earns a greater amount of interest by $486.12 compared to the investment with simple interest.

To determine which investment earns a greater amount of interest, we need to calculate the interest earned in both scenarios and compare the results.

1. Simple Interest:

The formula for simple interest is given by: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

Using this formula, we can calculate the interest earned with simple interest:

I = 100,000 * 0.03 * 4

I = $12,000

2. Compound Interest:

The formula for compound interest is given by: A = P * (1 + r/n)^(n*t), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period.

In this case, the interest is compounded annually, so n = 1. Let's calculate the amount earned:

A = 100,000 * (1 + 0.03/1)^(1*4)

A = 100,000 * (1.03)^4

A = $112,486.12

The interest earned in the compound interest scenario is A - P = $112,486.12 - $100,000 = $12,486.12.

The difference between the amounts of interest earned by the two investments is:

$12,486.12 - $12,000 = $486.12.

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Answer:

faction is 4/10

sorry don't know the rest

Answer:

To find the surface area of a pyramid

Step-by-step explanation:

The equation is used to find the surface area of a pyramid.

Answer:

The Answer Is 60

Answer:

60

Step-by-step explanation:

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60

5 10 15 20 25 30 35 40 45 50 55 60

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  \("2x + 3 = 9"\) states that the word  \("2x + 3"\) Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations \("x2 + 2x - 3 = 0\)  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  \(20\) of her time napping.

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Answer:

60

Step-by-step explanation:

To find area just multiply base time height, length time width, or side time side if it is a square, so 5 x 12 = 60

Answer:

12 units²

Step-by-step explanation:

A(triangle) = 1/2(2)(2) = 2 units²

A(triangle) = 1/2(2)(6) = 6 units²

A(Square) = 2(2) = 4 units²

A(Shape) = 2 + 6 + 4 = 12 units²

Answer:

D.

Step-by-step explanation:

The graph of 3 sin x will stretch vertically sin x by a factor 3. So 3 sin x will have a maximum value of 3 and a minimum of -3.

So it is either C or D.

The  -1 in the parentheses will move the graph 1 unit to the right and as the graph of y = sin x passes through the origin, the required graph will pass through (1, 0) - so it  is Graph D.

Answer:

D.

Step-by-step explanation:

We can cancel out choice A and choice B because both graphs' amplitude are 2. (Amplitude determines the max-min so if amplitude is 2 then max is 2 and min is -2)

Now for graph C and D, if we do not know how does sine graph shift, we will do substitution to find value of y when x = a.

Let's try x = 0 because both graphs have different y-value for x = 0.

\( \displaystyle \large{y = 3 \sin(x - \frac{\pi}{4} ) } \\ \displaystyle \large{y = 3 \sin(0 - \frac{\pi}{4} ) } \\ \displaystyle \large{y = 3 \sin( - \frac{\pi}{4} ) }\)

Let's recall the negative measure;-

\( \displaystyle \large{ \sin( - x) = - \sin(x) }\)

Therefore:-

\( \displaystyle \large{y = - 3 \sin( \frac{\pi}{4} ) } \\ \displaystyle \large{y = - 3 \cdot \sin( \frac{\pi}{4} ) }\)

We know that π/4 is equivalent to 45° because π is defined as 180° and 180°/4 is 45°

Using hand method, sin(45°) is √2/2

\( \ \displaystyle \large{y = - 3 \cdot \frac{ \sqrt{2} }{2} } \\ \ \displaystyle \large{y = \frac{ - 3\sqrt{2} }{2} }\)

Looks like when we substitute x = 0, the y-value becomes negative.

The only graph that's reasonable is D.

Another method is you substitute x = π/4 in which would make y-value = 0.

Since π/4 is between 0 < x < π/2, the graph D is correct because graph C may have amplitude of 3 but y-value does not become 0 when substitute x = π/4

So D.

Answer:

a).2x-6-5x-12x. this is answer

The standard deviation is 1.0319

x values between 10.4681 and 12.5319 are respectively ( 11 , 12 )

The probability that the number of granite specimens selected for analysis is within 1 standard deviation of its mean value is 0.6740

We are given that: a geologist has collected 14 specimens of basaltic rock and 14 specimens of granite.

Thus total rocks = N = 14 +14 = 28

The geologist instructs a laboratory assistant to randomly select 23 of the specimens for analysis.

Thus sample size = n = 23

Part a) What is the pmf of the number of granite specimens selected for analysis?

x = the number of granite specimens selected

Thus M = Number of granite specimens = 14

Thus x can have the following values:

x n-x = 23-x

9 14

10 13

11 12

12 11

13 10

14 9

We can select a minimum 9 granite specimens, so that total becomes 9 granite specimens + 14 basaltic rock = 23

and maximum 14 granite specimens, so that total becomes 14 granite specimens + 9 basaltic rock = 23

Here x = the number of granite specimens selected follows Hypergeometric distribution with parameters N = 28 ,M=14 , n = 23 .

P(X=9) =0.02037

Similarly, we find all next probabilities:

x P(x)

9 0.0204

10 0.1426

11 0.3370

12 0.3370

13 0.1426

14 0.0204

Part b) What is the probability that all specimens of one of the two types of rock are selected for analysis?

the probability that all specimens of one of the two types of rock are selected

That is:

P( All 14 are granite specimens and rest 9 are basaltic rock OR All 14 are basaltic rock and rest 9 are granite specimens)=......?

That is:

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =......?

From above table in part a) , we have:

P( 14 granite specimens) = 0.0204 , that means

P(14 granite specimens , 9 basaltic rock) = 0.0204

and

P( 9 granite specimens)=0.0204

That is:

P( 14 basaltic rock , 9 granite specimens) = 0.0204

Thus

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) =0.0204 + 0.0204

P( 14 granite specimens , 9 basaltic rock OR 14 basaltic rock , 9 granite specimens) = 0.0408

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The surface areas of the figures are 336, 82 and 836

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

The figures

For the triangular prism, we have

Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12

Surface area = 336

For the rectangular prism, we have

Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)

Surface area = 82

For the cylinder, we have

Surface area = 2π * 7 * (7 + 12)

Surface area = 836

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The surface area of the prisms are

1. 336 cm²

2. 82 m²

3. 836 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of prism is expressed as;

SA = 2B +pH

where B is the base area , p is the perimeter and h is the height.

1. SA = 2B +ph

B = 1/2 × 6 × 8

= 24 m²

p = 6+8+10 = 24m

h = 12m

SA = 2 × 24 + 24 × 12

= 48 + 288

= 336 cm²

2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)

= 2( 6+21+14)

= 2( 41)

= 82 m²

3. SA = 2πr( r +h)

= 2 × 3.14 × 7( 7 + 12)

= 44( 19)

= 836 cm²

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Answer:

\((a)\ c = \frac{1}{15}\)

\((b)\ 40\%\)

\((c)\ 60\%\)

Step-by-step explanation:

The given parameters can be represented as:

\(P_Y(y) \ge 0, y =1,2,3,4,5\)

\(P_y(y) = cy, y=1,2,3,4,5\)

Solving (a): The value of c

To do this, we make use of the following rule;

\(\sum\limit^5_{y=1}P_Y(y_i) = 1\)

Given that:

\(P_y(y) = cy, y=1,2,3,4,5\)

This is translated to:

\(c*1 + c * 2 + c * 3 + c * 4 + c * 5 = 1\)

\(c + 2c + 3c + 4c + 5c = 1\)

\(15c = 1\)

Solve for c

\(c = \frac{1}{15}\)

(b) The proportions of applications that requires at most 3 forms

This implies that: y = 1,2,3

So, we make use of:

\(P(Y \le 3) = P(Y=1) + P(y=2) + P(Y=3)\)

Recall that:

\(P_y(y) = cy, y=1,2,3,4,5\)

Substitute \(c = \frac{1}{15}\)

\(P_y(y) =\frac{1}{15}y\)

So:

\(P(Y \le 3) = P(Y=1) + P(y=2) + P(Y=3)\)

\(P(Y\le 3) = \frac{1}{15} * 1 +\frac{1}{15} * 2 +\frac{1}{15} * 3\)

\(P(Y\le 3) = \frac{1}{15} +\frac{2}{15} +\frac{3}{15}\)

Take LCM

\(P(Y\le 3) = \frac{1+2+3}{15}\)

\(P(Y\le 3) = \frac{6}{15}\)

\(P(Y\le 3) = 0.4\)

Express as percentage

\(P(Y\le 3) = 0.4*100\%\)

\(P(Y\le 3) = 40\%\)

(c) The proportions of applications that requires between 2 and 4 forms (inclusive)

This implies that: y = 2,3,4

So, we make use of:

\(P(2 \le Y \le 4) = P(Y=2) + P(Y=3) + P(Y=4)\)

\(P(2 \le Y \le 4) = 2 * \frac{1}{15} + 3 * \frac{1}{15} + 4 * \frac{1}{15}\)

\(P(2 \le Y \le 4) = \frac{2}{15} + \frac{3}{15} + \frac{4}{15}\)

Take LCM

\(P(2 \le Y \le 4) = \frac{2+3+4}{15}\)

\(P(2 \le Y \le 4) = \frac{9}{15}\)

\(P(2 \le Y \le 4) = 0.6\)

Express as percentage

\(P(2 \le Y \le 4) = 0.6 * 100\%\)

\(P(2 \le Y \le 4) = 60\%\)

Answer:

convert the lengths to meters

10dm=1m

1dm=0.1m

hence, firs ribbon

2m+0.1m=2.1m

Second Ribbon

3m and 9dm

convert 9dm into Metres we get 0.9m

hence, 3m+0.9m=3.9m

Third Ribbon

6m+0.4m=6.4m