Evaluate the expression
3(3a-1)+2, for a=2

B. 3

triangles only have 3 lines of symmetry and circles have infinite

Answer:

6

Step-by-step explanation:

60/10=6

Hope this helps :)

Answer:

A.  parallelogram

Step-by-step explanation:

It's not a rectangle because all 4 angles are not 90

It's not a rhombus because all 4 sides are not equal.

It's not a square because all 4 sides are not equal and all 4 angles are not 90.

It's a parallelogram because it's a quadrilateral with 2 pairs of opposite sides that are parallel.

The value of the expression when j=-2 and k=-1 is 8.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

Let's substitute j=-2 and k=-1 in the given expression and simplify it:

(jk⁻²/j⁻¹k⁻³)³

= ((-2)(-1)⁻²)/((-2)⁻¹(-1)⁻³))³ // Substitute j=-2 and k=-1

= ((-2)/(1/(-1)²))/((-1/(-1)³)))³

= ((-2)/1)/(-1/1))³

= (-2)/(-1))³

= 8

Therefore, the value of the expression when j=-2 and k=-1 is 8.

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Answer:

3

Step-by-step explanation:

By using distance formula

√(x2-x1)^2+(y2-y1)^2

√(5-5)^2+(4-1^2

√0+(3)^2

√9

=3

Answer:

Step-by-step explanation:

(n-2) x 180 = 1260

n-2 = 1260/180

n-2 = 7

n = 9

Therefore, the regular polygon has 9 sides.

Associative property holds for all types of numbers  and associative properties holds true addition as well as multiplication but not true for subtraction as well as division.

A number system is defined as a system of writing to express numbers.

The associative property holds for all types of numbers including real numbers, complex numbers, integers, fractions, and even irrational numbers.

There is no type of number for which the associative property does not hold.

associative properties holds true addition as well as multiplication but not true for subtraction as well as division.

Hence, associative property holds for all types of numbers  and associative properties holds true addition as well as multiplication but not true for subtraction as well as division.

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Let's use "j" to represent the cost per pound of jelly beans, and "t" to represent the cost per pound of trail mix.

From the first sentence of the problem, we can write an equation for the total cost of 8 pounds of jelly beans and 4 pounds of trail mix:

8j + 4t = 37

From the second sentence of the problem, we can write an equation for the total cost of 3 pounds of jelly beans and 2 pounds of trail mix:

3j + 2t = 15

Now we have two equations with two variables, which we can solve using algebra.

Multiplying the second equation by 4, we get:

12j + 8t = 60

We can now use the first equation to solve for one of the variables in terms of the other. Solving for j, we get:

j = (37 - 4t)/8

Substituting this expression for j into the second equation, we get:

3(37 - 4t)/8 + 2t = 15

Multiplying both sides by 8 to eliminate the fraction, we get:

111 - 12t + 16t = 120

4t = 9

t = 2.25

Substituting this value for t into the expression we found for j, we get:

j = (37 - 4(2.25))/8 = 2.125

Therefore, the cost per pound of jelly beans is $2.125 and the cost per pound of trail mix is $2.25.

Let x be the cost per pound of jelly beans and y be the cost per pound of trail mix. Then we can set up two equations:

8x + 4y = 37 (equation 1)

3x + 2y = 15 (equation 2)

We can solve for x and y by using the substitution method. Solve equation 2 for y:

y = (15 - 3x) / 2

Substitute this into equation 1:

8x + 4((15 - 3x) / 2) = 37

Simplify and solve for x:

8x + 30 - 6x = 37

2x = 7

x = 3.5

Now we can substitute x = 3.5 back into equation 2 to find y:

3(3.5) + 2y = 15

10.5 + 2y = 15

2y = 4.5

y = 2.25

Therefore, the cost per pound of jelly beans is $3.50 and the cost per pound of trail mix is $2.25.

Question #14:

Find the work done by the force field, [tex]\vec F(x,y,z)= < x-y^2, \ y-z^2, \ z-x^2 >[/tex],

on a particle that moves along the line segment from (0,0,1) to (3,1,0).

The parametrized form of a line is given as,

[tex]x=x_0+v_xt[/tex]

[tex]y=y_0+v_yt[/tex]

[tex]z=z_0+v_zt[/tex]

Where [tex](x_0,y_0,z_0)[/tex] is a point the line passes through and [tex]\vec v= < v_x,v_y,v_z >[/tex] is the direction of the line.

[tex]\Longrightarrow \vec v= < 3-0,1-0,0-1 > \Longrightarrow \boxed{ \vec v= < 3,1,-1 > }[/tex]

[tex]\Longrightarrow \boxed{(x_0,y_0,z_0)=(0,0,1)}[/tex]

[tex]z=-t+1, 0\leq t\leq 1[/tex]

This would imply that, [tex]dx=3dt,dy=dt,dz=-dt[/tex]

[tex]Work, W=\int\limits^a_b {\vec F(x,y,z) \cdot} < dx,dy,dz > \,dt[/tex]

[tex]\Longrightarrow \vec F(x,y,z)= < 3t-t^2, \ t-(-t+1)^2, \ -t+1-(3t)^2 >[/tex]

[tex]\Longrightarrow \boxed{\vec F(x,y,z)= < 3t-t^2, \ -t^2+3t-1, \ -9t^2-t+1 > }[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [ < 3t-t^2, \ -t^2+3t-1, \ -9t^2-t+1 > \cdot} < 3,1,-1 > ] \,dt[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [( 3t-t^2)(3)+(-t^2+3t-1)(1)+(-9t^2-t+1)(-1) ] \,dt[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [ 9t-3t^2-t^2+3t-1+9t^2+t-1 ] \,dt[/tex]

[tex]\Longrightarrow W=\int\limits^1_0 { [5t^2+13t-2 ] \,dt[/tex]

Using the power rule to integrate: [tex]\frac{d}{dx}[x^n]=nx^{n-1}[/tex]

[tex]\Longrightarrow W=\frac{5}{3}t^3+\frac{13}{2}t^2-2t \left. \right|_{0}^1[/tex]

[tex]\Longrightarrow W=[\frac{5}{3}(1)^3+\frac{13}{2}(1)^2-2(1)]-[0][/tex]

[tex]\Longrightarrow W=\frac{5}{3}+\frac{13}{2}-2[/tex]

[tex]\Longrightarrow \boxed{ W=\frac{37}{6}} \therefore Sol.[/tex]

Question #15:

Given:

[tex]w_m=170 \ lb[/tex]

[tex]w_c=25 \ lb[/tex]

[tex]w_m+w_c=195 \ lbs[/tex]

[tex]r_s=25 \ ft[/tex]

[tex]h_s=90 \ ft[/tex]

[tex]1 \ rev. =2\pi \Rightarrow 3 \ rev. =\bold{6\pi}[/tex]

Find:

[tex]W= \ ?? \ ft-lbs[/tex]

Equation:

[tex]W=\int\ {\vec F \cdot } \, d\vec r \Longrightarrow W=\int\ {[\vec F(\vec r(t)) \cdot r'(t)}]dt[/tex]

[tex]\vec F(x,y,z)= < 0,0,195 > \ and \ r(t)= < 25cos(t),25sin(t),\frac{90}{6\pi}t >[/tex]

[tex]r'(t)= < -25sin(t),25cos(t),\frac{15}{\pi} >[/tex]

[tex]\Longrightarrow W=\int\ {[\vec F(\vec r(t)) \cdot r'(t)}]dt[/tex]

[tex]\Longrightarrow W=\int\ {[ < 0,0,195 > \cdot < -25sin(t),25cos(t),\frac{15}{\pi} > ]dt[/tex]

[tex]\Longrightarrow W=\int\ {[ (195)(\frac{15}{\pi}) ]dt[/tex]

[tex]\Longrightarrow W=\int\ {\frac{2925}{\pi} dt[/tex]

Limits: [tex]0\leq t\leq 6\pi[/tex]

[tex]\Longrightarrow W=\int\limits^{6\pi}_0 {\frac{2925}{\pi} } \, dt[/tex]

[tex]\Longrightarrow W= {\frac{2925}{\pi}t \left. \right|_{0}^{6\pi}[/tex]

[tex]\Longrightarrow W= [{\frac{2925}{\pi}(6\pi)]-[0][/tex]

[tex]\Longrightarrow \boxed{W= 17,550 \ ft-lbs} \therefore Sol.[/tex]

Let me know if these were correct! As I strive to give the most accurate answers! Thank you.

Answer: 9

Step-by-step explanation:

Use the pythagorean thrm, a^2+b^2=c^2.

x^2+12^2=15^2 so x=sqrt(15^2-12^2)=9

Answer:

The answer to your problem is, B. 9 feet

Step-by-step explanation:

The pythagoras' theorem states that:

Hyp² = base² + perp²

Which can only be applicable for a right-angle triangle.

So by the ‘ Pythagoras' theorem ‘

Hyp² = base² + perp²

Base² = Hyp² - perp²

Base² = 15² - 12²

Base² = 225 - 144

Base² = 81

Base = 9

9 being the answer.

Thus the answer to your problem is, B. 9 feet

We get a negative number, which means that Rocco does not have enough money to make the purchase. In fact, he is short by $158.

An equation is a mathematical statement that shows that two expressions are equal. Equations are used to represent relationships between variables and to solve problems in various fields such as mathematics, physics, engineering, and economics. In an equation, there are typically two sides separated by an equals sign (=). The expressions on each side of the equals sign may include variables, constants, mathematical operations, and functions. The goal of solving an equation is to find the value(s) of the variable(s) that make both sides of the equation equal.

Here,

If Rocco has only $192 in his savings account and the set of golf irons costs $350, then he does not have enough money to buy the golf irons.

To see why, we can subtract the price of the golf irons from Rocco's savings:

$192 (Rocco's savings) - $350 (price of golf irons) = -$158

Therefore, Rocco does not have enough money to buy the set of golf irons with the remaining amount in his savings account.

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a. For the supermarket manager, the mode is one that  is the right tool as the appropriate form of the measure of central tendency as it would tell them which type of lettuce that was bought most often.

b. For the students, the mean is one that will be the right measure of central tendency as it would give them the idea of the average of all their test scores.

c. For the real estate agent, the median is one that is be the right measure of central tendency as it would tell them the selling price that is in the middle of all the given comparable houses.

Lastly, The student that is known to be is reporting the mean as the average. , this is one that tends to misrepresents their course performance due to the fact that the mean is affected by outliers for example as the 75%, 70%, and 55% scores. The median is one that can give a better representation of their performance.

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See text below



1. Here are three examples where the mean, median, and mode can be used to describe a situation. Which measure of central tendency would you use for each one? Why? (Don't forget the why.)

a. A supermarket manager wants to know how many types of lettuce customers purchase most often.

b. Students want to know the average of all their test scores in a certain grading period.

c. A real estate agent wants to set the selling price of a three-bedroom house so that there are as many comparable houses above as below the price. 2. A student's parents promise to pay for next semester's tuition if an A average is earned in chemistry. With examination grades of 97%, 97%, 75%, 70%, and 55%, the student reports that an A average has been earned. Which measure of central tendency is the student reporting as the average? How is this student misrepresenting the course performance with statistics?

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4) D

The first option is correct. When the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified the result is -x² + 3x - 8.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

We shall simply the polynomial -3x² + 2x - 4 - (-2x² - x + 4) as follows:

open bracket;

-3x² + 2x - 4 + 2x² + x - 4

group like terms;

-3x² + 2x² + 2x + x - 4 - 4

- x² + 3x - 8.

Therefore, the polynomial -3x² + 2x - 4 - (-2x² - x + 4) is simplified to give the result is -x² + 3x - 8.

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Answer: Barry would save approximately $15,208.08 by paying off the loan 8 years early.

Step-by-step explanation:

To calculate how much Barry would save by paying off the loan 8 years early, we first need to calculate the total amount of interest he would pay over the remaining 8 years.

We can use the formula for calculating the remaining balance on a loan:

Balance = (P * ((1 + r/n)^(nt)) - (A * (((1 + r/n)^(nt)) - 1)/(r/n)))

where:

P = principal amount (initial loan amount)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = time (in years)

A = monthly payment

Substituting the given values in the formula, we can calculate the remaining balance:

Balance = ($55,000 * ((1 + 0.068/12)^(1220)) - ($419.84 * (((1 + 0.068/12)^(1220)) - 1)/(0.068/12)))

Balance = $31,019.97

Now, we need to calculate the total interest paid over the remaining 8 years. We can do this by subtracting the remaining balance from the total amount of interest that would be paid over the entire 20-year loan term:

Total interest paid over 20 years = (A * 12 * 20) - P

Total interest paid over 20 years = ($419.84 * 12 * 20) - $55,000 = $50,969.63

Total interest paid over the remaining 8 years = (A * 12 * 8) - Balance

Total interest paid over the remaining 8 years = ($419.84 * 12 * 8) - $31,019.97 = $35,761.58

Therefore, Barry would save approximately $15,208.08 by paying off the loan 8 years early.

For a lower-tailed test, the critical value is:

[tex]z_c_r_i_t_i_c_a_l=-2.33[/tex]

Hypothesis tests can be right-tailed, left-tailed, or two-tailed. Depending on the test queue, the critical value changes. For left-tail hypothesis tests, the critical value obtained is negative.

Test for Population Proportion:

α = 0.01 (Significance level)

Critical value of test statistic, [tex]z_\frac{\alpha }{2}[/tex]

[tex]z_\alpha[/tex] value is the z − value having an area of α(0.0100) to the right.

The cumulative area to the left is 1 − α = 1 − 0.0100 = 0.9900.

Calculus of zα/2 using the cumulative standard normal distribution table

We search through the probabilities to find the value that corresponds to

0.9900.

We do not find 0.9900 exactly; the nearest value is corresponding  to 0.9901

Therefore,

[tex]z_\alpha =2.3+0.03[/tex]

[tex]z_\alpha =2.33[/tex]

For a lower-tailed test, the critical value is:

[tex]z_c_r_i_t_i_c_a_l=-2.33[/tex]

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The given question is incomplete and also incomplete in figure , so i take similar question:

Determine the critical value for a left-tailed test regarding a population proportion at the alpha = 0.01 level of significance.

the equation function in the form y = ab^x that passes through the points (2,12) and (3,24) is: [tex]y = 3(2)^x[/tex]

What is Cartesian coordinate?

A coordinate system, also known as a Cartesian coordinate system, is a system used to describe the position of points in space. It is named after the French mathematician and philosopher René Descartes, who introduced the concept in the 17th century. In a coordinate system, each point is assigned a unique pair of numbers, called coordinates, that describe its position relative to two perpendicular lines, called axes. The horizontal axis is usually labeled x and the vertical axis is usually labeled y.

Using the point (2,12), we get:

[tex]12 = ab^2[/tex]

Using the point (3,24), we get:

[tex]24 = ab^3[/tex]

Dividing the second equation by the first equation, we get:

[tex]24/12 = ab^3/ab^22 = b[/tex]

Substituting b = 2 into either of the two equations, we can solve for a:

[tex]12 = a(2)^2a = 3[/tex]

Therefore, the equation function in the form y = ab^x that passes through the points (2,12) and (3,24) is: [tex]y = 3(2)^x[/tex]

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Answer:

The y-value of the function is 4 in the table when the x-value is 0 after framing the linear equation.

Step-by-step explanation:

- Hope this helps

1. The 99% confidence interval is from 877.094 to 942.906.

2. The 99% confidence interval is from 883.267 to 936.733.

3. The 99% confidence interval is from 838.437 to 981.563.

What is interval?

In statistics, an interval refers to a range of values in which a population parameter, such as the mean or proportion, is estimated to lie with a certain level of confidence.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(20/√21) = 877.094

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(20/√21) = 942.906

Therefore, the 99% confidence interval is from 877.094 to 942.906.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(40/√21) = 883.267

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(40/√21) = 936.733

Therefore, the 99% confidence interval is from 883.267 to 936.733.

Using the t-distribution with 20 degrees of freedom and a 99% confidence level (two-tailed), we find the t-value from Appendix D to be 2.861.

The 99% confidence interval for the population mean is:

lower bound = [tex]\bar{x}[/tex] - t*(s/√n) = 910 - 2.861*(80/√21) = 838.437

upper bound = [tex]\bar{x}[/tex] + t*(s/√n) = 910 + 2.861*(80/√21) = 981.563

Therefore, the 99% confidence interval is from 838.437 to 981.563.

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Since these inequalities contradict each other, there is no value of b that satisfies both.

We have,

Starting with the first inequality:

2b - 8 > 5

Adding 8 to both sides:

2b > 13

Dividing by 2:

b > 6.5

Moving on to the second inequality:

3b + 13 < 9

Subtracting 13 from both sides:

3b < -4

Dividing by 3:

b < -4/3

So, we need to find a value of b that satisfies both b > 6.5 and b < -4/3. Since these inequalities contradict each other, there is no value of b that satisfies both.

Therefore,

Since these inequalities contradict each other, there is no value of b that satisfies both.

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Tally's probability of being on the red team is 1/4, or 0.25 when represented as a decimal.

Each team has four students because there are four equal-sized teams.

So Tally's chances of being on the red team are 4 (the number of students on the red team) divided by 16 (the total number of students):

4/16 = 1/4

As a result, Tally's likelihood of being on the red team is 1/4, or 0.25 when represented as a decimal.

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The corresponding p-value is 0.147 rounded to three decimal places.

Now, For find the p-value, we need to use a t-distribution with (n - 1) degrees of freedom,

where n is the sample size.

Since n = 50,

Hence, we have;

n - 1 = 50 - 1 = 49 degrees of freedom.

Hence, Using a t-table or calculator with 49 degrees of freedom, we find that the p-value for a t-statistic of -1.07 is approximately 0.147.

Therefore, the corresponding p-value is 0.147 rounded to three decimal places.

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The equation that represents line perpendicular to y = 2x - 4 is: D. y = -(1/2)x + 5

The equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

Now, let us write each of the given equations in slope intercept form to get:

A. y = 2x - 3

B. y = -(1/2)x + 3/2

C. y = 2x + 5/2

D. y = -(1/2)x + 5

E. y = (1/2)x - 7

Now, the given equation is:

y = 2x - 4

Thus, the slope that is perpendicular to it will be the negative reciprocal which is: -1/2.

Thus, option D is correct

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The value of X+z whose ratio is given above would be = 44

The ratio between three figures are given such as;

X:y:z = 3:6:8

Therefore,

if y = 6

X = 3

the y = 24

X = ?

make X the subject of formula;

X = 24×3/6

= 12

if y = 6

z = 8

then y = 24

z = ?

Make z the subject of formula;

z = 24×8/6

= 32

therefore X +Z= 12+32 = 44.

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The probability of choosing a green marble first and a blue marble second is 2/15 or approximately 0.133.

The multiplication rule of probability, which states that the probability of two distinct events occurring simultaneously is the product of their individual probabilities, must be utilized in order to resolve this issue.

We need to determine the probability of the sequence GB, which means selecting a green marble first and a blue marble second, after denoting the event of choosing a green marble as G and the event of selecting a blue marble as B.

Expecting that the primary marble isn't supplanted before the subsequent draw, the likelihood of picking a green marble on the main draw is P(G) = 4/10, since there are four green marbles out of ten taken care of.

Nine marbles, including three blue ones, will remain in the bag after the first marble is selected.

Given that the first marble was green, the probability of selecting a blue marble on the second draw is therefore P(B|G) = 3/9, as there will be three blue marbles out of the remaining nine.

Using the multiplication rule, the probability of the sequence GB is:

P(GB) = P(G) * P(B|G) = (4/10) * (3/9) = 2/15

Therefore, picking a green marble first and a blue marble second has a chance of 2/15, or roughly 0.133.

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Answer:

There are 6 cards, 5 of which do not have the number 4.

So P(not 4) = 5/6 = 83.3%

A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

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The total number of students is 2960.

35% of students went to Disneyland and 1924 of students went to Knotts.

Therefore, the total number of student can be calculated as follows:

The total number of student is the total number of student that went to Disneyland and Knotts.

let

x = total number of student

Therefore,

35% of x = Student that went to Disneyland

Hence,

65% of x = 1924

65 / 100 x = 1924

cross multiply

65x = 192400

divide both sides of the equation

x = 192400 / 65

x =   2960

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Answer:

Step-by-step explanation: