Find the volume of the composite solid

Answer:

19. Angelique=0.3, Jamila=0.1  20.15.2

Step-by-step explanation:

19 Angelique=0.3

          Jamila=0.1

20.

[tex]x^{2} =8.7^{2}+12.5^{2} \\x^{2} =231.94\\x=15.229...\\x=15.2[/tex]

[[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]]

The product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].

To calculate the product of two matrices, multiply each row of the first matrix with each column of the second matrix. Begin by multiplying the first row of the first matrix [-2, 0] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values -2, 0, 10, 2, 0 which will be the first row of the product matrix.

Next, multiply the second row of the first matrix [1, -1] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values 1, -1, 9, 2, -1 which will be the second row of the product matrix.

Therefore, the product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
The given matrices are:
[[-2, 0],
[1, -1]]
[[-1, 0, 5, 1, 0],
[1, -1, 3, 1, -1]]

To find the product of two matrices, we need to follow a few steps:

Multiply the first row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the first row of the first matrix by the second column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the second column of the second matrix, and then add the results.

By following these steps, we can obtain the product of the matrices. So, we can proceed as follows:

-2×(-1) + 0×1 = 2
-2×0 + 0×(-1) = 0
1×(-1) + (-1)×1 = -2
1×0 + (-1)×(-1) = 1

Hence, the product of the given two matrices is:
[[2,0,10,2,0],
[-2,2,-8,-2,2]]

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The area of the figure composed of a rectnagle and a triangle is 128in².

The figure in the the image is composed of rectangle and a triangle.

The area of a rectangle = length × width

Area of a triangle = 1/2 × base × height

Hence;

Area of the composite figure will be;

A = area of a rectangle + area of a triangle

From the image;

Now, we solve for thr area of the composite figure.

A = area of a rectangle + area of a triangle

A = ( 12in × 9in ) + ( 1/2 × 5in × 8in )

A = ( 108in² ) + ( 20in² )

A = 128in²

Therefore, the total area of the figure id 128 squared inch.

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The solution set in interval notation, 19(7 − x) ≥ 88 − 14x, is (-∞, 9]

To solve the inequality 19(7 - x) ≥ 88 - 14x, we will first distribute the 19 on the left side of the inequality and then combine like terms to isolate the variable x.

19(7 - x) ≥ 88 - 14x
133 - 19x ≥ 88 - 14x
-5x ≥ -45
x ≤ 9

Now, we can write the solution set in interval notation. Interval notation uses brackets or parentheses to indicate the endpoints of an interval. Brackets indicate that the endpoint is included in the interval, while parentheses indicate that the endpoint is not included.

Since x is less than or equal to 9, the solution set in interval notation is (-∞, 9]. This means that any value of x less than or equal to 9 will satisfy the inequality.

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Answer:

Step-by-step explanation:

I can't see anything.

Answer:4/5 and y = 9/5.

Step-by-step explanation:We can start by substituting the second equation into the first equation, replacing y with 1/2x+8:

3x + 4(1/2x+8) = 36

Simplifying, we get:

3x + 2x + 32 = 36

Combining like terms, we get:

5x + 32 = 36

Subtracting 32 from both sides, we get:

5x = 4

Dividing both sides by 5, we get:

x = 4/5

Now that we have found x, we can substitute it back into the second equation to find y:

y = 1/2x + 8 = 1/2(4/5) + 8 = 9/5

Therefore, the solution to the system of equations is x = 4/5 and y = 9/5.

Austin would have approximately $2,108 more than Josiah.

Approximately means "nearly" or "close to" an exact amount or number. It is often used to describe a quantity that is not exact, but can be estimated or rounded off. For example, "There were approximately 25 people in the room" means that the number was close to 25, but not necessarily exactly 25.

Using the formula A = P(1 + r/n)^nt, where P is the principal amount, r is the interest rate, n is the number of times compounded, and t is the number of years, we can calculate the amount of money Austin and Josiah would have in 17 years.
For Austin: A = $92,000(1 + 5.875/365)^365*17 = $120,308.05
For Josiah: A = $92,000(1 + 0.0575)^17 = $118,200.43
Therefore, Austin would have approximately $2,108 more than Josiah.

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Answer:

B. Left 2 units, down 9 units

Step-by-step explanation:

You would determine the x value by making the equation for x equal to 0. In this case we have x + 2 = 0. Subtract 2 from both sides to get x = -2. Determine the y value by the last digit which is -9. You now have the coordinate -2, -9, which is left 2 units and down 9 units.

Answer: there 28/29 days

Step-by-step explanation:

Answer: 28/29

Step-by-step explanation:

28 Days

29 Days for a leap year

The best possible equation of the line of best fit would be →

y = 8.6x + 10.5.

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data

Given is a scatter plot as shown in the image.

For the given graph the correlation is positive. So, we can write the slope of the line of the best fit as positive. So, we can write the equation of the line of best fit as → y = 8.6x + 10.5.

Therefore, the best possible equation of the line of best fit would be →

y = 8.6x + 10.5.

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Answer:

kindly update the question

The mean of the values will be 9.4, the median will be 3 points and the mode will be 4

It should be noted that mean in mathematics simply means the total added values of all the data in a set of divided by the number of days in a set.

The mean of the values will be:

= (10 + 8 + 11 + 12 + 6) / 5

= 47 / 5

= 9.4

The median of the set of numbers is the number on the middle when arranged ascending or in a descending manner. This is 3 points. The mode is 4.

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Answer:

For two linear equations : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0;

To determine if two such straight lines are parallel, then you should check for the following conditions :

a₁/a₂ = b₁/b₂ ≠ c₁/c₂ , where a,b are coefficients of x and y for each line.

if this condition is true for the coefficients of x,y, and the intercept of lines (c₁ and c₂) then they are parallel.

for instance,

let's say we have two lines :

x + 2y - 4 = 0,

2x + 4y - 12 = 0;

Now to check if they are parallel you simply check if the condition for parallel lines is met or not.

for these two lines :

a₁ = 1 , b₁ = 2, and c₁ = -4;

a₂ = 2, b₂ = 4, and c₂ = -12;

evaluating the values in the condition we have :

[tex]\frac{1}{2}[/tex] = [tex]\frac{2}{4}[/tex] ≠[tex]\frac{-4}{-12}[/tex] ;

since the condition for parallel is true for these two lines, we can conclude they are parallel.

Answer:

x to the power of 67000 to the 5th power.

Step-by-step explanation:

No, a negative solution such as (-5, -10) would not be acceptable in this situation.

Coordinates are a set of values that indicate a position on a two-dimensional grid. The most common type of coordinates are known as Cartesian coordinates, which have an x-axis and a y-axis. Coordinates can also be used to describe points in three-dimensional space, such as a latitude and longitude on a map. Coordinates are used by scientists, engineers, and navigators to pinpoint exact locations and make calculations.

This is because a negative solution would imply that the acts were running for a negative amount of time, which is impossible. Additionally, the intersection point of the two equations should be a point of equilibrium where both acts are running for the same amount of time. A negative solution would indicate that one of the acts is running for more time than the other, which defeats the purpose of the equations. Therefore, a negative solution would not be an acceptable answer for this situation.

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The correct answer is c. Failed to reject the null hypothesis.

Failed to reject the null hypothesis.

Explanation:

In this problem, we are given the price of drugs for human doses and animal doses from different pharmacies. We are asked to form a statistical decision using the p-value method. The null hypothesis is that the prices for the animal doses are equal to the prices for the human doses, while the alternative hypothesis is that the prices for the animal doses are significantly less than the prices for the human doses.


To form a statistical decision, we need to compare the p-value with the level of significance (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.


In this case, the level of significance is 1% (α=0.01). Since the p-value is not given in the problem, we cannot make a decision. Therefore, the correct answer is c. Failed to reject the null hypothesis.

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Step-by-step explanation:

steps are in the image above

The equation of the red graph is g(x) = x² + 3.

Option C.

The equation of the red graph can be determined by considering upscaling or transformation on the x - axis.

Since the equation focuses on the function g(x) and not on upscaling in the y-axis, any changes should not affect the x-axis. Therefore, we can eliminate (x - 3)² and (x + 3)² from the options given, since they involve modifying the x-axis.

In conclusion, as the transformation involves increasing the y-values along the y-axis, the correct choice is x² + 3 rather than x² - 3.

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There are three possible triangles that can be formed using the given measurements.

Measurement is the process of quantifying or comparing the amount, size, or extent of something. It is an important concept for scientists, engineers, and other professionals in order to compare and understand the world around them. Measurement involves the use of physical tools, such as rulers, scales, and protractors, and mathematical equations, such as formulas and equations.

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 43^2 + 15^2 - 2(43)(15)\cos(123^\circ)$\\$b^2 \approx 799.5$\\$b \approx 28.3$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.977$\\$A \approx 79.4^\circ$\\$B \approx 23.6^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=79.4^\circ$[/tex], [tex]$B=23.6^\circ$[/tex], [tex]$C=77^\circ$[/tex], [tex]$a=43$[/tex], [tex]$b\approx 28.3$[/tex] , and [tex]$c=15$[/tex].

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 36^2 + 47^2 - 2(36)(47)\cos(47^\circ)$\\$b^2 \approx 1666.5$\\$b \approx 40.8$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.647$\\$A \approx 40.9^\circ$\\$C \approx 92.1^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=40.9^\circ$[/tex], [tex]$B=47^\circ$[/tex], [tex]C\approx 92.1^\circ, a\ =36$[/tex], [tex]$b\approx 40.8$[/tex],

We can use the Law of Cosines to solve for the missing side:

[tex]h^2 = k^2 + p^2 - 2kp\cos(K)\\$h^2 = 47^2 + 10^2 - 2(47)(10)\cos(139^\circ)$\\$h^2 \approx 2363.7$\\$h \approx 48.6$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

So the triangle is [tex]$\triangle KHP$[/tex] were [tex]$K=139^\circ$[/tex], [tex]$H\approx 56.5^\circ$[/tex], [tex]$P\approx 124.5^\circ$[/tex], [tex]$k=47$[/tex], [tex]$h\approx 48.6$[/tex], and [tex]$p=10$[/tex].

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Answer:

If applying the 20% off coupon and the 10% coupon it would be separate. This would be different than a 30% coupon

Step-by-step explanation:

Let's say you are taking 20% off of $100, doing that would reduce the price to $80 because you took off $20, after this you would apply the 10% off coupon to the $80, your total would be 72 now because 10% of 80 is 8. The 20% Coupon and the 10% coupon stacked would bring your total to $72. If you flat out took 30% out of 100 dollars you would be left with $70 compared to the $72 that you got with the 20% coupon and the 10% coupon.

20% + 10% would remove less than a 30% coupon because after applying the 20% coupon, your 10% coupon would remove less because of the lower number being subtracted. Hope this helps

Answer:

1286.3934 kg

Step-by-step explanation:

Convert 153% to a decimal:

153 / 100 = 1.53

Multiply 840.78 by 1.53:

840.78 * 1.53 = 1286.3934

The formula for the nth term of the arithmetic sequence is 3(3n-1) or -3+9n(option B)

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.

The nth term of a n arithmetic sequence is given as:

a(n) = a+(n-1)d

where a is the first term and d is the common difference

a = 6

d = 15-6 = 9

a(n) = 6+( n-1) 9

= 6+9n -9

a(n) = 9n-3

a(n) = 3(3n-1)

therefore the formula for the nth term of the sequence is 3(3n-1)

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The response to the given question would be that Hence, 2 is the proportionality constant between y and x.

Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.  

We must calculate the ratio of the change in y to the change in x in order to discover the constant of proportionality between two variables, x and y. The slope of the line that depicts the connection between x and y is another name for this.

The slope of the line, which is the change in y divided by the change in x, is therefore equal to the constant of proportionality between y and x. As we can see from the graph, y grows by 2 units for every unit rise in x. Hence, the line's slope is 2/1, or only 2.

Hence, 2 is the proportionality constant between y and x.

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it definitely should be (-2,3)

Answer: 137.8 cm

Step-by-step explanation:

Using Pythagorean's Theorem, a² + b² = c², we can find the length of one of the braces.

Plug in your values:

115² + 76² = c²

13225 + 5776 = c²

19001 = c²

√19001 = c

c ≈ 137.8 cm

The braces are 137.8 cm long.

Hope this helps!

Answer:

Traduction:

Ann and Barbara are comparing their ages. They find that Barbara is the age that Ann was when Barbara was the age that Ann was when Barbara was half the age that Ann is today. If the sum of their current ages is 44 years, what is Ann's age today?

Soit x l'âge d'Ann aujourd'hui.

On sait que l'âge de Barbara est x - (x/2) = x/2 (car Barbara avait la moitié de l'âge d'Ann lorsque l'écart d'âge entre elles était de x/2).

On sait également que l'âge d'Ann lorsque Barbara avait x/2 ans est (x/2 - x) = -x/2 ans de moins que son âge actuel.

Donc, l'âge d'Ann lorsque Barbara avait l'âge qu'avait Ann à ce moment-là est x - (x/2) - (-x/2) = 2x/2 = x ans.

Ainsi, l'âge de Barbara aujourd'hui est également x ans.

La somme de leurs âges actuels est 44 ans, donc :

x + x = 44

2x = 44

x = 22

Donc, l'âge d'Ann aujourd'hui est 22 ans.

The scientific notation or representation of expression (2.5 X 1/10²)(4.2 X 10⁶) is equal to 10.5×10⁴.

Scientific notation is a way of writing very large or very small numbers. Numbers are written in scientific notation as a number from 1 to 10 multiplied by a power of 10.For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸. 

Scientific notation is utilized by scientists, mathematicians, and engineers whilst they may be operating with very huge or very small numbers

Solution for scientific notation according to the information given:

(2.5 X 10^-2)(4.2 X 10⁶) = 2.5 ×(1/10²) × 4.2 × 10⁶

                                        = 2.5 × 4.2 × 10⁴

                                        = 10.5 × 10⁴

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The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.

To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:

5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0

Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:

[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]

Finally, we can combine these rows into a single matrix to get the augmented matrix:

[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

This is the augmented matrix for the given system of equations.

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The measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

The interior angles of a quadrilateral are measured as A \( 51^{\circ} 22^{\prime} 30^{\prime \prime} \), B \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \), C \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \), and D \( 124^{\prime} 46^{\prime \prime} \).

To find the measure of angle D, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.

Add the measures of angles A, B, and C:
\( 51^{\circ} 22^{\prime} 30^{\prime \prime} \) + \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \) + \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \) = \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \)

Subtract the sum of angles A, B, and C from 360 degrees to find the measure of angle D:
360^{\circ} - \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \) = \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \)

Therefore, the measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

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Answer:

Step-by-step explanation:

1 ticket costs 1 × $4.50 = $4.50

2 tickets cost 2 × $4.50 = $9.00

3 tickets cost 3 × $4.50 = $13.50

4 tickets cost 4 × $4.50 = $18.00

The first table is the only one that matches these values.