(1) 6/6 ✓ (2) 4- 12 cm 9 cm The shape below is made from 4 of these triangles. 15 cm, Work out the area of the shape. Diagram NOT accurately drawn 888 Diagram NOT accurately drawn Onk 20 21-1744-8 30x4+2=6 (7+7)+2-​

a) Approximately 778.7 grams of thorium 234 will be left after 0.5 years.

b) Approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

(a) To find the amount of thorium 234 left after 0.5 years, we can use the equation:

[tex]A_t = A_0 e^{(-10.498t)}[/tex]

where A₀ is the initial amount, which is 1000 grams, t is the time in years, and At is the amount after t years.

Substituting t = 0.5, we get:

[tex]At = 1000 e^{(-10.498\times0.5)} = 778.7 \ grams[/tex]

Therefore, approximately 778.7 grams of thorium 234 will be left after 0.5 years.

(b) To find the time at which 115 grams of thorium 234 will be left, we can use the same equation and solve for t:

[tex]A_t = A_0 e^{(-10.498t)[/tex]

Dividing both sides by A₀ and taking the natural logarithm of both sides, we get:

ln(At/A₀) = -10.498t

Substituting At = 115 grams and A₀ = 1000 grams, we get:

ln(115/1000) = -10.498t

Solving for t, we get:

t = (ln(115/1000)) / (-10.498) ≈ 2.1 years

Therefore, approximately 2.1 years will have passed when 115 grams of thorium 234 are left.

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Answer:

∠ BCA = 25°

Step-by-step explanation:

the inscribed angle BCA is half the measure of the central angle BOA , so

∠ BCA = [tex]\frac{1}{2}[/tex] × 50° = 25°

Answer: 3 1/3

Step-by-step explanation:

if the width of the rectangle is equal to “x” then the length is equal to 3x+2

The area is 40ft^2

so: 40=(3x+2)(x)

Then we simplify and subtract 40 in both sides:

0=3x^2+2x-40

Then we will use the quadratic formula to solve for x

X=(-2-sqr(2^2-4(3)(-40)))/2*3

And

X=(-2+sqr(2^2-4(3)(-40)))/2*3

then x is either equal to 3 1/3 or -4, since the answer cannot be negative, the answer is 3 1/3

The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together. E.g. The measurements here are in centimetres so the surface area is measured in square centimetres ( c m 2 ) (cm^2) (cm2)

triangle-

Base Surface Area = 112

= 121 feet2

Lateral Surface Area =

2×11× √

( 11 )2 + 72

2

= 195.84943196241 feet2

Total Surface Area = 316.84943196241 feet2

bottom bit-

Surface Area = 2×(15×5 + 15×8 + 5×8) = 470 feet2

The number of unique preferences represented in the table is given as follows:

B. Five.

Unique outcomes are the outcomes that appear in a data-set, however we only count them twice.

For example, if João and Elisa are Buffalo Bills fans, while Chanel and Laura are Atlanta Falcons fans, we have two unique outcomes(Bills and Falcons fans).

Hence the outcomes for this problem is given as follows:

Hence the number of unique outcomes is given as follows:

5.

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The student would spend $18 on books and lab manuals.

An expenditure refers to the spending of money on something or the money that is spent on something.

Total Expenditure = Lab fee + Materials fee + Tuition + Books and lab manuals + Tools

Total Expenditure = 8% + 10% + 38% + 18% + 26%

Total Expenditure = 100%

We will calculate the amount spent on books and lab manuals. The amount spent on books and lab manuals is:

= (Books and lab manuals percentage / Total Expenditure percentage) * $100

= (18% / 100%) * $100

= 0.18 * $100

= $18.

Missing details:

On pie chart  for School Expenditures; Lab fee = 8% Materials fee =10% Tuition = 38% Books and lab manuals = 18% Tools = 26%

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The probability of spinning a quadrilateral is 1/3 and probability of spinning a polygon with at least 5 sides is 0.5

Probability is a measure of the likelihood of an event to occur.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

In the given problem, we can determine the probability of each event by following this simple formula.

a. The probability of spinning a quadrilateral.

P(quadrilateral) = 2 / 6 = 1/3

NB: A quadrilateral is any figure or shape with four sides.

b. The probability of a polygon with at least 5 sides.

P(polygon > 5 sides) = 3/6 = 1/2

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Solution of function is,

⇒ x ∈ [- 7, 5]

We have to given that;

The function is,

⇒ f(x) = x² + 2x - 35

We can simplify for f (x) ≤ 0 as;

⇒ f(x) = x² + 2x - 35

⇒ x² + 2x - 35 ≤ 0

⇒ x² + 7x - 5x - 35 ≤ 0

⇒ x (x + 7) - 5 (x + 7) ≤ 0

⇒ (x + 7) (x - 5) ≤ 0

⇒ x ∈ [- 7, 5]

Thus, Solution of function is,

⇒ x ∈ [- 7, 5]

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The 3 consecutive odd numbers are 5, 7, and 9

3 consecutive odd numbers can be written as:

x

x + 2

x + 4

Such that x is an odd number.

Here we want that 4 times the middel number is equal to 14 more than the sum of the first and the third, then we can write the linear equation:

4*(x + 2) = x + x + 4 + 14

Solving this for x, we will get:

4x + 8 = 2x + 18

4x - 2x = -8 + 18

2x = 10

x = 10/2 = 5

The 3 numbers are 5, 7, and 9

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The equivalent monthly interest rate is 1.91%

To determine the value, we need to know the formula for simple interest, we have that;

I = PRT/100

Such that the parameters of the formula are;

From the information given , we have that;

The annual interest rate R = 23%

Then, to determine its equivalent monthly, we get;

If 12 months = 23%

Then 1 month = x%

cross multiply the values, we have;

12x = 23

Divide by the coefficient

x = 23/12 = 1. 91%

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Answer:

y=3x−9

Step-by-step explanation:

Answer:

a)  Very strong positive correlation (r = 0.99).

b)  y = 299.46 + 1.74x

c)  $1,709 per month

Step-by-step explanation:

Linear regression is a statistical technique used to model the relationship between a dependent variable and an independent variable by fitting a linear equation to the observed data points. It aims to find the line of best fit that minimizes the overall distance between the observed data and the predicted values based on the linear equation.

We can use a statistical calculator to perform linear regression analysis on the given data.

The explanatory (independent) variable is the square footage (x-values).

The response (dependent) variable is monthly rent (y-values).

After entering the data into a statistical calculator we get:

The r-value, also known as the correlation coefficient, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

In this case, an r-value of 0.99 suggests that there is a very strong positive linear relationship between between square footage and monthly rent. As the square footage increases, the monthly rent tends to increase as well.

This high correlation indicates that square footage is a strong predictor of monthly rent. However, it is important to note that the correlation coefficient alone does not imply causation or provide information about the underlying factors influencing the relationship.

[tex]\hrulefill[/tex]

To determine the regression equation, substitute the found values of a and b into the regression line formula, y = a + bx.

Round the values of a and b to the nearest hundredth:

Therefore, the regression equation is:

[tex]\boxed{y = 299.46 + 1.74x}[/tex]

where:

[tex]\hrulefill[/tex]

To determine the monthly rent that we might expect to pay for an 810 square foot apartment, substitute x = 810 into the regression equation found in part (b), and solve for y:

[tex]\begin{aligned}y &= 299.46 + 1.74(810)\\&=299.46+1409.4\\&=1708.86\\&=1709\end{aligned}[/tex]

Therefore, we would expect to pay approximately $1,709 per month for an 810 square foot apartment.

Step-by-step explanation:

Sometimes it is hard to 'see' the factorization....so you can take the HCF out of the three terms to perhaps see it better:

Factor out a '4'

4* ( 2n^2 + 17n + 21  )

4 ( 2n +3 )(n +7 )                    DONE.

Answer: Hey i'd love to help you can you please provide the choices that are given?

Step-by-step explanation:

Answer:

[tex]x\leq -5[/tex]

1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

To find Daniela's Season 3 pay in terms of p, we need to calculate the pay increase for each season.

In Season 2, her pay increases by 5 percent, which means she will receive 105 percent (or 1.05) of her Season 1 pay.

In Season 3, her pay increases by 10 percent from Season 2, so she will receive 110 percent (or 1.10) of her Season 2 pay.

To express Daniela's Season 3 pay in terms of p, we multiply the Season 1 pay (p) by the pay increase factors for Season 2 and Season 3:

Season 2 pay = 1.05p

Season 3 pay = 1.10(1.05p) = (1.10)(1.05)p

Simplifying the expression, we get:

Season 3 pay = 1.155p

Therefore, 1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

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3) Sin B = 5/9.43, Cos B = 8/9.43, Tan B = 5/9.43

4) Angle A is 40 degrees

5) x is  23.8 mm

A specific type of triangle known as a right triangle has a single angle that is exactly 90 degrees, or a right angle. The sides that make up the right angle are the legs and the hypotenuse.

The Pythagorean theorem connects the side lengths of a right triangle by stating that the square of the hypotenuse's length is equal to the sum of the squares of the legs' lengths.

Cos A = 47/61

A = Cos-1(47/61)

= 40 degrees

5) The marked side can be obtained from;

Cos 28 = 21/x

x = 21/Cos 28

x = 23.8 mm

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The annual deposit for John for total amount of annuity is A = $ 29,060.29

Given data ,

To determine the annual deposit amount needed for John to have a total of $500,000 by the time he retires, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where FV is the future value, P is the annual deposit, r is the annual yield (interest rate), and n is the number of years.

In this case, we are given:

FV = $500,000

r = 5% = 0.05

n = 25 years

Substituting these values into the formula, we have:

$500,000 = P * [(1 + 0.05)^25 - 1] / 0.05

And , the value of P is

P = ($500,000 x 0.05) / [(1.05^25) - 1]

P ≈ ($25,000) / (1.858734... - 1)

P ≈ ($25,000) / 0.858734...

P ≈ $29,060.29

Hence , John must deposit approximately $29,060.29 into the retirement account each year to accumulate a total of $500,000 by the time he retires in 25 years

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The mass of the milk with a density of 1.03 g/cm³ is 417.15 g.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

To determine the mass of the milk, plug the given values into the above formula and simplify.

p = m / v

m = p × v

m = 405 × 1.03

m = 417.15 g

Therefore, the mass is 417.15 grams.

Option D) 417.15 g is the correct answer.

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Hello!

it's a multiplication

The measure of angle θ is 210°. Therefore, the value of the cos θ will be -√3 / 2.

Given that:

sin θ = -0.5

The angle θ lies in the third quadrant.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The angle θ is calculated as,

sin θ = -0.5

θ = 210°

The value of the cosine of anlge θ is calculated as,

cos θ = cos 210°

cos θ = -√3 / 2

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Here is the descriptive statistics table for the four variables, including skew and kurtosis for each variable:

Variable Mean Median Standard Deviation Skewness Kurtosis

Height 68.2 68.0 3.0 0.2 -0.6

Weight 170.0 168.0 30.0 0.4 -0.6

Age 25.0 25.0 2.0 0.0 -1.0

IQ 100.0 100.0 15.0 0.0 -1.0

The skewness and kurtosis values for all four variables are close to 0, which suggests that the data is approximately normally distributed.

In addition to the descriptive statistics table, we can also assess normality by creating a histogram of the data.

The histograms for height, weight, and age are all approximately bell-shaped, which suggests that the data for these variables is approximately normally distributed. However, the histogram for IQ is slightly skewed to the right, which suggests that the data for IQ may not be truly normally distributed.

Overall, the descriptive statistics and histograms suggest that the data for height, weight, and age is approximately normally distributed.

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Hello!

1 book => [tex]1^{\frac{3}{8} }[/tex]

14 books => [tex]14*1^{\frac{3}{8} }[/tex]

[tex]14*1^{\frac{3}{8} }\\\\= 14 * 1\\\\ \boxed{=14}[/tex]

The answer is 14 inches thick.

The group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.

According to the given chart, calculate that each crate contains a total of 48000 calories. Therefore, two missing crates result in a total loss of 96000 calories (48000 x 2).

Determining whether the group has enough food to reach the South Pole and return to base camp, calculate the total number of calories required for the entire trip. Supposing a round trip of 10 days to the South Pole and back, the total number of calories required would be:

Total Calories = (6000 calories/person x 5 people x 10 days) x 2 (round trip)

Total Calories = 600,000 calories

To cover for the lost calories, the group would need to sacrifice one member's trip to the South Pole and send them directly back to base camp. This would leave four members to continue to the South Pole, where they would have to ration their food carefully to make sure they have enough for the entire trip.

Below is a plan to ensure enough food:

Day 1-2:

Day 3-5:

Day 6-7:

Day 8-10:

Add up all the total calories consumed:

60,000 + 18,000 + 180,000 + 48,000 + 90,000 = 396,000 calories

This is less than the total calories required, which was 600,000 calories. Therefore, the group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.

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Answer:

dört yarım saat 2 saattir

Step-by-step explanation:

After considering the given data we conclude that the system of equations are x=-3 and y=2², under the condition that the given system of equations are x+2y=1 -3x-2y=5

considering the system of equations x+2y=1 and -3x-2y=5. The coefficient matrix is

| 1  2 |
| -3 -2 |

and its determinant is 1×(-2)-(-3)×2 = 4. The matrix obtained by replacing the first column by the right-hand sides of the equations is

| 1  2 |
| 5 -2 |

and its determinant is 1×(-2)-5×2 = -12. The matrix obtained by replacing the second column by the right-hand sides of the equations is

| 1  1 |
| -3 5 |

and its determinant is 1×5-(-3)×1 = 8. Therefore, x=-3 and y=2².
Cramer's rule consist of a  formula which is required for  solving a system of linear equations with as many equations as unknown variables, applying determinants. It expands the solution in terms of the determinant of the coefficient matrix and the matrices taken from it by replacing one column by the right-hand sides of the equations.
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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

Here, we have,

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer: The value of X is 12.

Step-by-step explanation:

K and M are parallel lines so,

6x-13 = 4x+11

Subtract 4x from both sides,

2x-13 = 11

Add the 13 to both sides,

2x = 24

Divide by 2,

x = 12

:).

Answer:

Step-by-step explanation:

6x - 13 = 4x + 11

2x = 11 + 13

2x = 24

x = 24 : 2

x = 12