Given PQ|| BC, what is PB?
9.6 units
10 units
13 units
14 units​

The sketches of the graphs are added as an attachment and the gradient of the perpendicular line l₂ is 1

Given that

3x + 4y + 12 = 0

Set x = 0 to determine the y-intercept

4y + 12 = 0

So, we have

y-intercept = -3

Set y = 0 to determine the x-intercept

3x + 12 = 0

So, we have

x-intercept = -4

For the gradient, we make y the subject in 3x + 4y + 12 = 0.

y = -3/4x - 12/4

y = -3/4x - 3

So, the gradient is -3/4

The sketch of the graph is attached.

Here, we have the points P (-1,4) and Q (3,0).

The gradient is

gradient = (0 - 4)/(3 + 1)

gradient = -1

From the point, we have

x-intercept = 3

For the y-intercept, we have

(0 - 4)/(3 + 1) = (y - 4)/(0 + 1)

(y - 4)/(0 + 1) = -1

y - 4 = -1

y-intercept = 3

So, the equation is

y = -x + 3

The sketch of the graph is attached.

We understand that l₂ is perpendicular to l

The gradients of perpendicular lines are

Gradient 1 = -1/Gradient 2

So, we have

l₂ = -1/-1

Evaluate

l₂ = 1

Hence, the gradient of line l₂ is 1

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I'm sorry, but I cannot answer this question without additional information about the dimensions of the capsule. Please provide me with the necessary information so that I can assist you.

a) The exponential growth function for a city's population that was 6.53 million in 2012 with an exponential growth rate of 2.79% per year is y = 6.53(1.0279)^t.

b) Based on the exponential growth function y = 6.53(1.0279)^t the population of the city in 2018 is 7.7 million.

c) The population of the city will be 10 million in 2028.

d) The doubling time for the population is 25 years.

An exponential growth function is one of the two exponential functions, including an exponential decay function.

An exponential growth function shows the relationship between two variables with an exponent and exhibits a constant rate of growth per period.

Population of the city in 2012 = 6.53million

Exponential growth rate = 2.79% per year

Let the number of growth years = t

a) y = 6.53(1.0279)^t

b) From 2012 to 2018, the number of years = 6 years

Population in 2018, y = 6.53(1.0279)^6

= 7.7 million

c) When the population will be 10 million = 15.5 years

10 = 6.53(1.0279)t

t = 15.5 years

= 16 years

= 2028

d) 13.06 = 6.53(1.0279)t

t = 25.189 years

= 25 years

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Answer:

90 degrees counterclockwise

The point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).

Given is a point, (8, 1) we need to find the coordinates of a point which is dilated from the origin by the scale factor of 2 and translation over the y-axis,

So, the coordinates of after dilation by k scale factor =

(x, y) = (kx, ky)

So, (8, 1) = (16, 2)

Now, the translation over the y-axis gives,

(x, y) = (-x, y)

Therefore, (16, 2) = (-16, 2)

Hence, the point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).

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Answer:

16.5 = 6

Step-by-step explanation:

The equation given is (+25)-5x5:2+2² = 27-5×5=2+2². When calculating, we first simplify the division to get (+25)-12.5+4 = 27-25+4. Then we add and subtract the values on either side to get 16.5 = 6. Finally, as the equation is incorrect, we can conclude that the initial assertion is false. It is important to carefully follow the order of operations and simplify expressions correctly to avoid errors in equations.

Answer: 75%

Step-by-step explanation:

     We will divide the wanted outcome by the total number of possible outcomes. Note that a decimal times 100 becomes a percentage.

[tex]\displaystyle \frac{\text{not picking a diamond card}}{\text{cards in the deck}} =\frac{39}{\text{52}} =0.75\;\;\;0.75*100=75\%[/tex]

You need 9 years to buy the car.

Given that, you need to $160,000, you have $58,000, the bank pays 6 % annual interest on its accounts. we need to find the number of years will it be before you have enough to buy the car,

A = P(1+r)ᵇ

102000 = 58000(1+0.06)ᵇ

1.75 = 1.06ᵇ

log 1.75 = b log 1.06

b = 9.6

Hence, you need 9 years to buy the car.

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Examining the graph, it can be deduced that the graph is not a function.

Domain and range are mathematical notation utilized to define the spectrum of possible accepted input values (domain) as well as the corresponding output values (range) in a given function or relation.

A definitive domain correspondingly denotes the compilations of all plausible inputs that generate a valid result when put essentially into the relation or operation.

Conversely, the range defines the plethora of conceivable outputs that this very same function or relation can devise, considering its specified domain.

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Answer:

  2035.8 ft³

Step-by-step explanation:

You want to know the volume of a cylinder with radius 6 ft and height 18 ft.

The volume of a cylinder is given by the formula ...

  V = πr²h

For the given dimensions, the volume is ...

  V = π(6 ft)²(18 ft) ≈ 2035.8 ft³

The volume of the cylinder is about 2035.8 cubic feet.

__

Additional comment

If you use 3.14 for π, you get 2034.7 cubic feet.

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Answer:

check attachment

Step-by-step explanation:

First write in point-slope form:

y-y1=m(x-x1)

Now substitute:

y-(-1)=3/4(x-(-4))

And then just solve. You should get a y-intercept of 2.

The area of the trapezoid with parallel sides of 8 meters and 7 meters, and a height of 4 meters, is 30 square meters.

To find the area of a trapezoid, we use the formula:

Area = (a + b)h/2

where "a" and "b" are the lengths of the parallel sides of the trapezoid, and "h" is the height of the trapezoid.

In this case, we are given that the parallel sides are 8 meters and 7 meters, and the height is 4 meters.

Substituting these values into the formula, we get:

Area = (8 + 7) x 4 / 2

= 15 x 4 / 2

= 60 / 2

= 30 square meters

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The decision meets each of the criteria by: Buying 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each enables the purchase of 700 frozen delights within the $400 budget and satisfies the objective of producing at least $800 in profit.

I have made the decision to buy 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each in order to fulfil the requirement of buying 700 frozen delights at a price of no more than $400.

Cost of purchasing 500 popsicles = (500 * $0.50)

Cost of purchasing 500 popsicles = $250

Cost of purchasing 200 ice cream sandwiches =(200 * $1.50)

Cost of purchasing 200 ice cream sandwiches  = $300

So, Total cost of purchasing all 700 frozen treats is $550 ($250 + $300) which is within the budget of $400.

I intend to sell the popsicles for $1.50 each and the ice cream sandwiches for $3.00 each in order to meet the requirement of turning a profit of at least $800. This would bring in $1350 in income for the ice cream sandwiches and $750 for the popsicles (500 * $1.50 and 200 * $3.00 respectively).

The objective of producing a profit of at least $800 is met after deducting the expense of buying the frozen treats from the overall income.

Net profit =($1350 - $550)

Net profit = $800

Therefore purchasing  500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each satisfies the objective of producing at least $800 in profit.

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the answer to your math problem is 2000

Answer:

-24√35

Step-by-step explanation:

Mark Brainliest!!

Answer:

there are no choices given but...

Step-by-step explanation:

this simplifies to 8/3, or 2 2/3

find the choice that isn't either of those ( is also 2.66666 repeating)

The required Mark has completed 38.46% of the race.

To calculate the percentage of the race completed by Mark, we can divide the number of miles he has run by the total length of the race and then multiply by 100 to convert the result to a percentage.

So, Mark has run 5 miles out of a total of 13 miles:

Percentage of race completed = (5/13) x 100%

Calculating this expression, we get:

Percentage of race completed = 38.46%

Therefore, Mark has completed 38.46% of the race.

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Answer:

-7≤y≤2

Step-by-step explanation:

The range measures the highest and lowest numbers up and down on the y-axis for a line. In order to determine range, start with the smallest number (the farthest place the line touches going down) then write less than or equal to. This is because the two dots are closed, meaning they include what the line touches. Afterward, add another less than or equal to, and then add the biggest number (the highest place the line touches going up). The range basically gives you your boundaries, and tells you how high or low the line you are describing is. And after that, you're done!

I hope this helps :)

The requried,  Celia made 15 mugs if she had 7.45 lbs of clay left over.

To determine the number of mugs that Celia made, we need to first subtract the weight of the sculpture and the leftover clay from the initial weight of the clay. This will give us the total weight of clay that Celia used for the mugs:

Total weight of clay used for mugs = 40 lbs - 17.4 lbs - 7.45 lbs = 15.29 lbs

Next, we can divide the total weight of clay used for the mugs by the amount of clay used per mug:

Number of mugs = Total weight of clay used for mugs / Amount of clay used per mug

Amount of clay used per mug = 1.01 lbs/mug

A number of mugs = 15.29 lbs / 1.01 lbs/mug = 15.13

Therefore, Celia made 15 mugs.

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The minimum height the second beaker must be so it does not overflow is 9.55 inches.

Given that a beaker has a radius of 1.8 inches and height of 4.6 inches. we need to find the height of another beaker which has the radius of 1.25 in and has same volume,

Volume of a cylinder = π × radius² × height

= 3.14 × 1.8² × 4.6

= 46.8 in³

Now, the second beaker =

46.8 = 3.14 × 1.25² × h

h = 46.8 / 3.14 × 1.25²

h = 9.55

Hence, the minimum height the second beaker must be so it does not overflow is 9.55 inches.

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The value of x in the triangle is 12.285.

We have,

We use cosine identities.

So,

Cos Ф = Base / Hypotenuse

Now,

Cos 35= x/15

0.819 = x/15

x = 0.819 x 15

x = 12.285

Thus,

The value of x is 12.285.

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Answer:

The answer is A.

A graph passes through a point if its equation is equal to the coordinate of this point. In this exemple:

5x+4y=8

we replace the variables with 4 and -3 (x with 4 and y with -3):

5(4)+4(-3)=8

20-12=8

8=8 so it passes.

NOW , for the slope:

slope = - 5/4 ( the equation is 5x+4y=8 , the cartesian equation is 5x+4y-8=0. THE cartesian equation with variables is ax+by+c=0) NOW this is linked with the slope bcz the slope is linked to the director vector (-b;a) that gives (-4;5), this is the director vector's formula that we're going to call U. THEN with this formula you get the slope: Y of U / X of U = 5/-4 = - 5/4 (bcz you dont leave the denominator with a negative sign).

THAT'S it thats the answer.

Based on the information, we cannot reject the null hypothesis because our calculated phi coefficient (0.245) is smaller than the critical value (3.84).

It should be noted that to establish whether the phi coefficient is statistically significant, we can compare it to a crucial value. However, the significance level (i.e., alpha) must be specified ahead of time.

Assume a 0.05 level of significance. We calculate the crucial value for a 2x2 contingency table with 1 degree of freedom and a significance level of 0.05 using a phi coefficient table or calculator.

We cannot reject the null hypothesis because our calculated phi coefficient (0.245) is smaller than the critical value (3.84). As a result, we find that there is no statistically significant relationship between the therapist's method and client satisfaction.

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The equation 2x² - 7x - 30 = 0 has two solutions: x = -5/2 and x = 6 and both solutions are real.

Given the equation in the question:

2x² - 7x - 30 = 0

We can use the quadratic formula to to determine the number and type of solutions :

x = (-b±√(b² - 4ac)) / (2a)

2x² - 7x - 30 = 0

a = 2

b = -7

c = -30

Plugging in these values, we get:

x = (-b±√(b² - 4ac)) / (2a)

x = (-(-7) ± √((-7)² - ( 4 × 2 × -30))) / (2×2)

x = (7 ± √( 49 - ( -240))) / (4)

x = (7 ± √( 49 + 240)) / (4)

x = (7 ± √( 289)) / (4)

x = (7 ± 17) / 4

x = (7 - 17) / 4 and x = (7 + 17) / 4

x = -5/2 and x = 6

Therefore, the two solutions are x = -5/2 and x = 6.

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Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.

Using chi-squared goodness-of-fit test with Benford's Law, observed check frequencies were found to be significantly different, indicating possible fraud. The test statistic was 756.153, exceeding the critical value of 15.51.

To test for goodness-of-fit with Benford's Law, we can use the chi-squared goodness-of-fit test. The null hypothesis is that the observed frequencies follow Benford's Law, while the alternative hypothesis is that they do not.

We can start by calculating the expected frequencies for each leading digit based on Benford's Law. According to Benford's Law, the expected proportion of leading digits is

P(d) = log10(1 + 1/d), where d is the leading digit (1, 2, ..., 9).

Then, we can calculate the expected frequencies by multiplying the proportion by the sample size

Expected frequency for digit d = P(d) * sample size.

Using this formula, we can calculate the expected frequencies for each digit

Expected frequencies: 3.542, 2.019, 1.518, 1.221, 1.028, 0.886, 0.778, 0.697, and 0.643.

We can use these expected frequencies and the observed frequencies to calculate the chi-squared statistic

chi-squared = Σ (observed frequency - expected frequency)² / expected frequency

We can then compare this value to the chi-squared distribution with 8 degrees of freedom (since there are 9 digits and one constraint, which is that the frequencies must add up to the sample size). Using a significance level of 0.05 and a chi-squared distribution table or calculator, the critical value is 15.51.

Plugging in the observed and expected frequencies, we get

chi-squared = (0 - 3.542)²/3.542 + (12 - 2.019)²/2.019 + (0 - 1.518)²/1.518 + (73 - 1.221)²/1.221 + (482 - 1.028)²/1.028 + (186 - 0.886)²/0.886 + (8 - 0.778)²/0.778 + (23 - 0.697)²/0.697 + (0 - 0.643)²/0.643

chi-squared = 756.153

Since the calculated chi-squared statistic (756.153) is greater than the critical value (15.51), we reject the null hypothesis and conclude that the observed frequencies are not consistent with Benford's Law. This suggests that the check amounts are the result of fraud.

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Answer:

y = 3/4x + 15

Step-by-step explanation:

Given;

A line passes through the point (-8, 9) and has a slope of 3/4

Question:

Write an equation in slope-intercept form for this line.​

Solve:

Slope-intercept form ⇒ y=mx+b

Which-

Based on the given;

Using slope intercept form to find y-intercept;

y=mx+b

9 = 3/4(-8) + b

9 = -6 + b

9+6 = -6+6 + b

b = 15

Therefore now we can write an equation.

y = 3/4x + 15

RevyBreeze

The value of length of AG is,

AG = 157.02

We have to given that;

AD = 31 cm

DC = 22 cm

Hence, We get;

AC = √31² + 22²

AC = √961 + 484

AC = √1445

AC = 38

Thus, We get;

cos 76° = AC / AG

0.242 = 38 / AG

AG = 38/0.242

AG = 157.02

Therefore, The value of length of AG is,

AG = 157.02

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a) The proportion of the investments had a return of between 10% and 30% is given as follows: 0.68 = 68%.

b) The proportion of the investments had a return of between -10% and 50% is given as follows: 0.997 = 99.7%.

c) The proportion of the investments had a return either less than 10% or more than 30% is given as follows: 0.32 = 32%.

d) The proportion of the investments had a positive return is given as follows: 0.9985 = 99.85%.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Hence the percentages for this problem are given as follows:

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Answer:

100

Step-by-step explanation:

the room is square this means each wall equal 25 .4 walls *25 =100 square feet

Answer:120

Step-by-step explanation: