A light in a park can illuminate effectively up to a distance of 100 m. A point on a bike path is 150 m from the light. The sight line to the light makes an angle of 23° with the bike path. What length of the bike path, to the nearest metre, is effectively illuminated by the light?

Answer:

120

Step-by-step explanation:

Corresponding angles of similar figures are congruent.

The measure for w is 120 degree.

We have ABCD ~ FECG

If two quadrilaterals are similar, it means that their corresponding angles are congruent, and their corresponding sides are proportional.

Then, we can write as

AB/ FE = CB/ EC = CD/ CD = AD/ FG

and, <A= <F,          

<B = <E,

<C= <C,

<D= <G

So, the measure for w is same as angle G.

Thus, the measure for w is 120 degree.

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Answer:

3 Cups of flour.

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

x/5 + 1 = 11
    x/5 = 10
        x = 50

[tex] \frac{9}{8 \: } = 1 \frac{1}{8} [/tex]

[tex] \sf \frac{9}{8} [/tex]

Step-by-step explanation:

[tex] \sf9 \div 8 = 1(1left)[/tex]

[tex]1 \frac{1}{8} [/tex]

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_______

Moumocl!

The statement fourth "The spread between the lower quartile and the median is greater than the spread between the upper quartile and the median" is correct.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

The box plot is missing.

The box plot is shown (please refer to attached picture)

The given options are:

As we know the property of box plot the difference between the lower and higher quartiles is greater than the difference between the upper and lower quartiles.

The spread between the lower quartile and the median:

= 15 - 9 = 6

= 19 - 15 = 4

Thus, the statement fourth "The spread between the lower quartile and the median is greater than the spread between the upper quartile and the median" is correct.

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The area of the wooden part of the frame is 4x² +20x +17 sq.cm , Area of a Rectangle is 4x² +2x-2 sq.cm .

A rectangle is a polygon with four sides . The opposite sides are parallel and equal.

It is given that the outside length and breadth is 4x + 5 centimeters and width 2x + 3 centimeters.

inside the frame has length and breadth 4x - 2 centimeters long and x + 1 centimeters wide.

The polynomial to describe the area of the picture window

The dimension of the inner picture frame is the dimension of the picture window

Area of a Rectangle = Length *  Breadth

Area of a Rectangle = (4x-2) (x+1) = 4x² +4x -2x-2 = 4x² +2x-2 sq.cm

The picture frame area without the window =

Area of the total picture frame - Area of the inner picture frame

= (4x+5)(2x+3) - (4x-2)(x+1)

= 8x² + 12x +10x+15 -4x²-2x +2

= 4x² +20x +17

The area of the wooden part of the frame is 4x² +20x +17 .

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Answer:

6x-2

Step-by-step explanation:

-4x(1-3)-(2x+2)

= 4x+12x-2x-2

6x-2

(simplify)

Answer:

6x - 2

Step-by-step explanation:

Edge

Answer:

131

Step-by-step explanation:

well, Diego is 4 now, so by his 18th birthday that'll be 14 years later.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1600\\ r=rate\to 8.25\%\to \frac{8.25}{100}\dotfill &0.0825\\ t=years\dotfill &14 \end{cases} \\\\\\ A=1600[1+(0.0825)(14)]\implies A=1600(2.155)\implies A=3448[/tex]

Using the Charles law, the following are the solutions to the problems;

1) 16 dm3

2) 170 K

3) 2.4 L

Charles law states that, the volume of a given mass of gas is directly proportional to the temperature at constant pressure.

For problem 1;

T1 = 20 + 273 = 293 K

V1 = 15 dm3

T2 = 318 K

V2 = ?

V1/T1 = V2/T2

V1T2 =V2T1

V2 = V1T2/T1

V2 = 15 dm3 * 318 K/293 K

V2 = 16 dm3

Problem 2

V1 = 250cm3

T1 = 10 + 273 = 283 K

V2 = 150cm3

T2= ?

T2 = V2T1/ V1

T2 =  150cm3 *  283 K/250cm3

T2 = 170 K

Problem 3

V1 = 2.3 L

T1 = 25 + 273 = 298K

V2 = ?

T2 = 40 + 273 = 313 K

V2 = V1T2/T1

V2 = 2.3 L * 313 K/298K

V2 = 2.4 L

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Amalia would be correct. They are guessing when the height would be 10, and you are given an equation that will 'predict' that. Height is y, so substitute 10 in the equation and solve for x. You will get x=6

Find the perimeter of the region.**

The circle are congruent to each other.

The circles are tangent to each other, and the straight

segments are tangent to the circles.

The straight

segments are 5 units long

Done!

Answer:

[tex](f+g)(x)=3x^3-2x^2+10x-12[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=3x^3-2x^2+4x-5\\g(x)=6x-7 \end{cases}[/tex]

[tex]\begin{aligned}(f+g)(x) & = f(x)+g(x)\\& = (3x^3-2x^2+4x-5)+(6x-7)\\& = 3x^3-2x^2+4x-5+6x-7\\& = 3x^3-2x^2+4x+6x-5-7\\& = 3x^3-2x^2+10x-12\end{aligned}[/tex]

Answer z=2

See picture attached for the math

Answer:

Step-by-step explanation:

Remark

The deck is divided into 4 different kinds of cards

clubs

diamonds

Hearts

Spades

Each kind of card has a 2

So there are 4 twos in a standard deck of cards.

Answer:

The experimental probability that the next patient will be female and in the age range 22-39 is 56/420

Probability is the odds that a random event would happen. The odds usually lie between 0 and 1.

The experimental probability = number of female in the age range 22-39 / total number of patients

=  56/420

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Answer:

22 inches

Step-by-step explanation:

3 feet = 36 inches

36-14=22

The other half is 22 inches long

Answer:

T10=108

Step-by-step explanation:

TN=bn+c

27,36,81=constant difference is 9

Tn=bn+c

Tn=9n+18

T10=9(10)+18

T10=90+18

T10=108.

hope it helps.

Answer: 2.703

Step-by-step explanation:

The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more is 0.036.

The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more will be:

= (26 + 8 + 2)/1000

= 36/1000

= 0.036

The significance level is set at 5%, and the probability of the result is statistically significant because the probability of the difference is less than 5% significance level.

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The value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The question is in the picture please refer to the attached picture.

We know the sum of all angles in a kite is 360 degree

110 + (5x) + 110 + 70 = 360

290 + 5x = 360

5x = 70

x = 14

Thus, the value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.

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Answer:

[tex]y = 3x - 6[/tex]

Step-by-step explanation:

Hello!

With an x - intercept of 2, the coordinate is (2, 0). With a y - intercept of -6, the coordinate is (0, -6).

We have to find the equation of the line that goes through these points.

The equation of a line is written in slope-intercept format: [tex]y = mx + b[/tex]

First let's find the slope using the slope formula: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Remember that a coordinate is written in (x, y) format.

So, we have the slope and the y - intercept. We can plug those into the equation.

The equation of the line is [tex]y = 3x - 6[/tex]

The linear regression equation that represents this data set is equal to y = 11.7x + 48.2 and an estimate of the calendar year is 2022.

First of all, we would determine the slope of the given data set by using this formula:

[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]

For the sample mean (years), we have:

∑x = 0 + 1 + 2 + 3

∑x = 6.

∑x² = 0² + 1² + 2² + 3²

∑x² = 14.

For the sample mean (profits), we have:

∑y = 46 + 57 + 84 + 76

∑y = 263.

∑xy = (0 × 46) + (1 × 57) + (2 × 84) + (3 × 76)

∑xy = 453.

Now, we can determine the slope:

[tex]Slope = \frac{4(453) - 6(263)}{4(14) - 6^2} \\\\Slope = \frac{234}{20}[/tex]

Slope, m = 11.7.

For the intercept, we have:

[tex]Intercept = \frac{14(263) - 6(453)}{4(14) - 6^2} \\\\Intercept = \frac{964}{20}[/tex]

Intercept, c = 48.2.

Therefore, the linear regression equation is given by:

y = 11.7x + 48.2.

Since the profit would reach 144,000 dollars, the calendar year would be calculated as follows:

144 = 11.7x + 48.2

11.7x = 144 - 48.2

11.7x = 95.8

x = 95.8/11.7

x = 8.2.

For the calendar year, we have:

Year = 2014 + 8.2

Year = 2022.2 ≈ 2022.

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If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.

Two of the components of GDP are government spending and private investment.

If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.

GDP would therefore increase.

This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.

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I went thru it and im pretty sure that only these work

-10

-5

-3

Answer:

V≈314

Step-by-step explanation:

* means times

volume of a cone

it's a right circular cone

formula

volume =

π * radius squared * (height ÷ 3)

π * 5 squared * (12 ÷ 3)

π * 25 * (4)

π * 100

3.14 * 100 = 314

factoid

pi or π in fraction form is 22/7

5 and 12 means the length of that

cone is 13

because it's a right circular cone

that means there's a right triangle

one of the special triangles is a

5,12,13 right triangle where

13 is the hypotenuse

moomoomath

Answer:

y - 2 = -5 (x - 1)

Step-by-step explanation:

Formula for point-slope equation :

y - y₁ = m (x - x₁)

============================================================

Given :

⇒ Point (x₁, y₁) = (1, 2)

⇒ Slope (m) = -5

=============================================================

Solving :

⇒ y - 2 = -5 (x - 1)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Equation of line can be written in point - slope form as :

[tex]\qquad \sf  \dashrightarrow \:y - y_1 = m(x - x_1)[/tex]

So, required equation is ~

[tex]\qquad \sf  \dashrightarrow \:y - 2 = - 5(x - 1)[/tex]

The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

Complex numbers are square root of negative numbers. They are expressed as a + bi

Using the expression

(4+7i)-2i(2+3i)

Expand

4 + 7i - 4i -2i(3i)

4 + 3i - 2(-3)

4 + 6 + 3i

10 + 3i

Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)

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The volume of the given sphere.

[tex]\large\boxed{Formula:V = \frac{4}{3} \pi {r}^{3}}[/tex]

[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve

Substitute the values according to the formula.

[tex]V = \frac{4}{3} \times 3.14 \times {8}^{3} [/tex]

[tex]V = 2143.573333 \: {cm}^{3} [/tex]

[tex]\large\boxed{= 2143.6 \: {cm}^{3} \: (nearest \: tenth)}[/tex]

Hence, the volume of the given sphere is 2143.6 cubic centimeters.

Answer: The answer is True .

The statement is false, these two ratios don't make a proportion.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

5/9, 56/99

we know, that, two ratios make a proportion if, a:b=c:d

but, here,

5/9= 5:9

56/99 = 56: 99

Hence, The statement is false, these two ratios don't make a proportion.

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