Ilana is training for a half marathon. For the first three days of her training plan, she will need to run 4.125 miles each day. For the next two days she will increase her mileage to 5.675 miles per day. How many miles total did Ilana run during her first training week?

The values of the matrices operations are [tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex] and [tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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

[tex]G = \left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right][/tex]

Also, we have

[tex]F = \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Using the above as a guide, we have

[tex]4G + 2F = 4\left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right] + 2 \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Evaluate the sum

[tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex]

Next, we have

[tex]D = \left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right][/tex]

Also, we have

[tex]B = \left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

The matrix expression is then represented as

[tex]4D - 3B= 4\left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right] - 3\left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

Evaluate

[tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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Answer:

C

Step-by-step explanation:

It mentions that they charge 1.20 per kg of lettuce

The type of distribution pictured in this histogram is skewed.

A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.

In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.

There are two types of skewed distributions: positively skewed and negatively skewed.

The distribution in the image is positively skewed as its is pulled towards the left.

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Answer:

  61°

Step-by-step explanation:

You want the angle XCA in the figure, given that angle XBA is 70°, and ABCD is a rectangle with AB=5.6m and BC=6.4m. Angles at A are right angles.

The length of diagonal AC is found using the Pythagorean theorem.

  AC² = AB² +BC²

  AC = √(5.6² +6.4²) = 0.8√113 ≈ 8.504 . . . . meters

The length XA is found using the tangent function:

  Tan = Opposite/Adjacent

  tan(B) = XA/AB

  XA = AB·tan(B) = 5.6·tan(70°) . . . . meters

The angle XCA is found from the tangent relation:

  tan(XCA) = XA/AC

  tan(XCA) = 5.6·tan(70°)/(0.8√113) = 7·tan(70°)/√113

  angle XCA = arctan(7·tan(70°)/√113) ≈ 61.07°

The angle XC makes with the horizontal is about 61°.

Based on the information, we identified that the scale used in the construction is approximately 1:35.2.

To find the scale used in the construction of the Crazy Horse Monument, we need to divide the height of the actual monument by the height of the model. Let's use the following formula to calculate the scale:

The height of the actual monument is 563 feet and the height of the scale model is 16 feet. Substituting these values in the formula, we get:

Simplifying the fraction, we get:

Therefore, the scale used in the construction of the Crazy Horse Monument is approximately 1:35.2.

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Answer:

300

Step-by-step explanation:

The size of matrix cM is given as follows:

9 x 10.

When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.

The parameters for this problem are given as follows:

Hence the size of matrix cM is given as follows:

9 x 10.

(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).

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Answer:

[tex] {z}^{2} - 10z + 9 = [/tex]

[tex](z - 1)(z - 9)[/tex]

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

The coefficient of determination, given the total variation and the explained variation would be 0.898.

R-squared, or the coefficient of determination, represents the proportion of variation within a response variable that can be explained by the regression model. This calculation is achieved through dividing the explained variation by the total variation.

We are given the explained variation as 18. 592. We are also given the total variation as 20. 711.

The coefficient of determination is:

= explained variation / total variation

= 18. 592 / 20.711

= 0. 898

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Full question is:

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119.

Find the coefficient of determination. Round to three decimal place

Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.

Since, When it comes to APR for a new or used vehicle loan, a borrower's credit score is one of the main factors considered by lenders.

The higher the credit score, the very more likely that a borrower is to be offered a lower APR.

Hence, In this case,

Tyler has a FICO score of 780 which is considered excellent, and is buying a used vehicle.

This combination of a high credit score and a used vehicle purchase makes Tyler the most likely candidate to be offered the lowest APR.

Thus, Tyler who is buying a used vehicle and has a FICO score of 780 is likely to be offered the lowest APR. The Option A is correct.

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Answer:

2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

Step-by-step explanation:

To divide 2 1/4 by 1 1/2, we first need to convert both mixed numbers to improper fractions:

2 1/4 = (2 × 4 + 1) / 4 = 9 / 4

1 1/2 = (1 × 2 + 1) / 2 = 3 / 2

Now we can divide by multiplying by the reciprocal of the second fraction:

(9/4) / (3/2) = (9/4) * (2/3)

We can simplify this multiplication by canceling the common factor of 3 in the numerator of the second fraction and the denominator of the first fraction:

(9/4) * (2/3) = (33/4) * (2/13) = 9/2

So 2 1/4 divided by 1 1/2 is equal to 9/2 or 4 1/2.

[tex]\boxed{\sf \dfrac{3}{2}}.[/tex]

[tex]\sf \dfrac{2\dfrac{1}{4} }{1\frac{1}{2} }[/tex]

[tex]\sf 2\dfrac{1}{4}\Longrightarrow\dfrac{4}{4} +\dfrac{4}{4} +\dfrac{1}{4} =\dfrac{4+4+1}{4} =\dfrac{9}{4}[/tex]

[tex]1\dfrac{1}{2} =\dfrac{2}{2} +\dfrac{1}{2} =\dfrac{2+1}{2} =\dfrac{3}{2}[/tex]

[tex]\sf \dfrac{\dfrac{9}{4} }{\dfrac{3}{2} }[/tex]

• Check the attached image.

[tex]\dfrac{9}{4} *\dfrac{2}{3}[/tex]

[tex]\dfrac{9*2}{4*3} =\dfrac{18}{12} \\ \\\dfrac{18/2}{12/2} =\dfrac{9/3}{6/3}=\boxed{\sf \dfrac{3}{2}} .[/tex]

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The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.

:: Radius of trundle wheel = 30 cm = 0.3 meter (as 100 cm = 1 m)

:: No. of rotations = 48

:: Circumference of a circle = ( 2 x π x r )

where, r is radius of the circle

So, as,

Distance between junctions = [ (circumference of trundle wheel) x (no. of rotations) ]

Therefore,

Distance = (2 x π x 0.3) x (48)

Distance = 2 x (3.14) x 0.3 x 48

Distance = 90.432 meters

When rounded off to the nearest meter,

Distance = 90 meters.

So, The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.

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The value of the height of the entire climbing frame is 11.99 feet

To determine the value, we need to know the different trigonometric identities.

These identities are;

From the information given, we have that;

In the triangle, the parameters are;

Hypotenuse is the distance between the architect and frame

The angle is 63.43

Adjacent is 6 feet

Using the tangent identity, we have;

tan 63.43 = h/6

cross multiply, we get;

h = tan (63. 43) × 6

Find the tangent value and substitute, we have;

h = 1. 99 × 6

Multiply the values, we have;

h = 11. 99 feet

Then, the height of the entire climbing frame is 11. 99 feet

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Complete question:

'The architect stands 6 feet from climbing frame, looking up at the top of the frame at an angle of 63.43" It is 5 and half feet from ground to the architect's eyes: The vertical distance from eye level to the top of the climbing frame is feet: The height of the entire climbing frame is feet:'

angle1 and angle3

angle6 and angle8

angle5 and angle7

Answer:

48 unit cube

Step-by-step explanation:

Solution Given:

For Triangle ABC

hypotenuse AB= 5

base AC=4

By using hypotenuse law

height BC=[tex]\sqrt{5^2-4^2} =3[/tex]

Now Area of the right-angled triangle is 1/2 * base*height

=1/2*AC*BC=1/2*4*3=6 units square

As we know that

The volume of triangular prism: Area of base * height

over here Area of the base= Area of the Triangle and the height is the length of the prism

=6 units square*CF

=6 units square*8

=48 unit cube

Answer:

The volume of the given prism is 48 cubic units.

Step-by-step explanation:

The volume of a prism can be calculated by multiplying the area of its base by its height.

The bases of the given prism are the congruent right triangles ABC and DEF.

We have been given the measures of sides AB and AC of triangle ABC.

To determine the area of ΔABC, we first need to calculate the measure of side BC using Pythagoras Theorem:

[tex]\implies AC^2+BC^2=AB^2[/tex]

[tex]\implies 4^2+BC^2=5^2[/tex]

[tex]\implies 16+BC^2=25[/tex]

[tex]\implies BC^2=9[/tex]

[tex]\implies BC=3[/tex]

The area of a triangle is half the product of its base and height.

The base and height of a right triangle are its legs.

[tex]\begin{aligned}\textsf{Area of base}&=\textsf{Area of $\triangle ABC$}\\\\&=\dfrac{1}{2} \cdot BC \cdot AC\\\\&=\dfrac{1}{2} \cdot 3 \cdot 4\\\\&=6\; \sf square\;units\end{aligned}[/tex]

Therefore, the area of the base of the prism is 6 square units.

Finally, to find the volume of the prism, multiply the area of the base by the height of the prism:

[tex]\begin{aligned}\textsf{Volume of prism}&=\textsf{Area of base} \cdot \sf height\\\\&=\textsf{Area of $\triangle ABC$} \cdot \overline{CF}\\\\&=6 \cdot 8\\\\&=48\; \sf cubic\;units\end{aligned}[/tex]

Therefore, the volume of the given prism is 48 cubic units.

Answer:

39270

Step-by-step explanation:

When the first person is picked, there is a 1 in 35 chance that it will be Person 1. If they are selected, that leaves 34 people left in the pool. After Person 2 is selected, there are 33 people left in the pool for Person 3.

35*34*33=39270

Answer:

True proportion of homeowners in the population lies between 0.333 and 0.847

Step-by-step explanation:

If 9 out of 22 randomly picked people said they rented their homes, then the remaining 13 must own their homes. Therefore, the point estimate of the proportion of homeowners is:

Point estimate = Number of homeowners / Total number of people surveyed

Point estimate = 13 / 22

Point estimate = 0.59 (rounded to two decimal places)

To calculate the 95% confidence interval for the true proportion of homeowners, we can use the following formula:

Confidence interval = Point estimate ± (Z-value x Standard error)

where the Z-value corresponds to the desired level of confidence and the standard error is given by:

Standard error = sqrt [ (Point estimate x (1 - Point estimate)) / Sample size]

For a 95% confidence interval, the Z-value is 1.96 (from the standard normal distribution). Using the point estimate obtained earlier, the sample size is 22, and we can calculate the standard error as:

Standard error = sqrt [ (0.59 x 0.41) / 22 ]

Standard error = 0.131 (rounded to three decimal places)

Substituting these values into the formula, we get:

Confidence interval = 0.59 ± (1.96 x 0.131)

Confidence interval = 0.59 ± 0.257

Confidence interval = (0.333, 0.847)

Therefore, with 95% confidence, we can say that the true proportion of homeowners in the population lies between 0.333 and 0.847.

Answer:

Subtract the powers, 8-4.

When you simplify that equation itself, the answer is 10,000.

So when you do 10⁴, it's 10,000.

Daniel incorrectly applied the square root to both terms on the left side of the equation and he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

Let's first look at the first equation that Daniel solved incorrectly:

25x²-16=9

Daniel's solution:

√(25x² )-√16=√9

5x-4=±3

5x=±7

x=±7/5

What Daniel did wrong here is that he incorrectly applied the square root to both terms on the left side of the equation.

Instead, he should have simplified the left side first, using the fact that √(a²) = |a|, before applying the square root. So the correct solution is:

25x²-16=9

25x²=25

x²=1

x=±1

Now let's look at the second equation that Daniel solved incorrectly:

z³-2=6

Daniel's solution:

z³=8

∛(z^3 )=∛8

z=±2

What Daniel did wrong here is that he forgot to take into account the possibility of multiple roots when solving for the cube root of z³.

In fact, z³ = 8 has three roots: z = 2, z = -1 + i√3, and z = -1 - i√3. So the correct solution is:

z³-2=6

z³=8

z=2

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The class mark of the modal class is: 25

From the given histogram, the following Frequency Distribution is obtained:

Class Interval Mid point Frequency

625-675 650 3

676-726 701 5

727 - 777 752 7

778 - 828 803 8

829 - 879 854 6

880 - 930 905 2

931 - 981 956 0

982 - 1032 1007 1

b. To find the lower class limit of the first class:

First class: 625

c. The upper limit of the first class is:

First class: 676

The class mark of the modal class is:

The modal class is: 803

The class mark is upper limit + lower limit/2

Thus, 828-778/2

=> 50/2

The class mark of the modal class is: 25

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An equation which Samantha can use to find the side length of the base in terms of the volume and height of her puzzle is: A. a = √(3V/h)

In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:

Volume of a square pyramid, V = 1/3 × a² × h

Where:

By making "a" the subject of formula, the side length of the base of a square pyramid can be determined as follows;

V = 1/3 × a² × h

3V = a²h

a² = 3V/h

By taking the square root of both sides of the equation, we have:

a = √(3V/h)

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Answer:

Step-by-step explanation:

However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent.  Negative version because to get to a decimal you move in the negative direction.

.1  =  1.0 x [tex]10^{-1}[/tex]

.01 = 1.0 x [tex]10^{-2}[/tex]

.001 = 1.0 x [tex]10^{-3}[/tex]

.000001  =,1.0 x [tex]10^{-6}[/tex]

Answer:

245 inches

Step-by-step explanation:

Yards->Inches

1 yard = 36 inches

Therefore, 6 yards = 36 x 6 = 216 inches

Feet->Inches

1 feet = 12 inches

Therefore, 2 feet = 2 x 12 = 24 inches

Adding all inches,

=> 216 + 24 + 5

=> 245 inches

Answer: A) Let's first calculate how far the van would have traveled in the half hour before the car started. The van's speed is 50 km/h, which means in half an hour it would have traveled 50/2 = 25 km.

Now let's consider the time it takes for the car to catch up to the van. We can represent this using the formula:

distance = rate × time

Let's call the time it takes for the car to catch up "t". We know that during this time, the van is also traveling. In fact, it has been traveling for t + 0.5 hours (the half hour before the car started plus the time it takes for the car to catch up). So the distance the van has traveled is:

distance van = 50 × (t + 0.5)

The distance the car has traveled is:

distance car = 60t

When the car catches up to the van, they will have traveled the same distance. So we can set the two distances equal to each other:

50(t + 0.5) = 60t

Simplifying this equation:

50t + 25 = 60t

Subtracting 50t from both sides:

25 = 10t

So t = 2.5 hours.

But we're not done yet! We need to add the 0.5 hours that the van traveled before the car started to get the total time it took for the car to catch up:

t + 0.5 = 2.5 + 0.5 = 3 hours

So the car catches up to the van 3 hours after the van started, or at 12:15 pm.

B) We can use the formula:

distance = rate × time

to find the distance between the two towns. We know the car traveled for 6 hours (from 9:45 am to 3:45 pm) and its speed was 60 km/h. So the distance it traveled is:

distance car = 60 × 6 = 360 km

We also know that the van traveled for 6.5 hours (from 9:15 am to 3:45 pm) and its speed was 50 km/h. So the distance it traveled is:

distance van = 50 × 6.5 = 325 km

The distance between the two towns is the difference between these two distances:

distance = distance car - distance van = 360 - 325 = 35 km

So the distance between the two towns is 35 km.

The quadratic equation is solved and the solution is x = 1 and x = 4

Given data ,

Let's expand the left-hand side of the equation:

(2x+1)² + (4x-4)²

= (2x)² + 2(2x)(1) + 1² + (4x)² - 2(4x)(4) + 4² (using the formula for the square of a binomial)

= 4x² + 4x + 1 + 16x² - 32x + 16

= 20x² - 28x + 17

Now let's expand the right-hand side of the equation:

(4x-1)²

= (4x)² - 2(4x)(1) + 1²

= 16x² - 8x + 1

Now we can set the left-hand side equal to the right-hand side and simplify:

20x² - 28x + 17 = 16x² - 8x + 1

4x² - 20x + 16 = 0

x² - 5x + 4 = 0

(x - 1)(x - 4) = 0

Hence , the solution is x = 1 and x = 4

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The area of the sector is 2π/1

The formula for calculating the area of a sector is expressed as;

A = θ/360 πr²

Given that the parameters are;

From the information given, we have that;

The angle = 45 degrees

radius, r = 4

Substitute the values, we have;

Area = 45/360 × π × 4²

Divide the values

Area = 3/ 24 × π × 16

Multiply the values, we have;

Area = 48π/24

Divide the values, we have;

Area = 2π/1

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Answer:

3.4.1) (8x^2)(6x^2 - 4x) = 48x^4 - 32x^2

3.4.2) 48x^4 - 32x^2 = (16x^2)(3x^2 - 2)

3.4.3) Length = 16(2^2) = 16(4) = 64

Width = 3(2^2) - 2 = 3(4) - 2

= 12 - 2 = 10

Area = 64(10) = 640