A plane intersecting a double-napped cone is perpendicular to the central axis. Which conic section is formed?

Answer:

Yes, there is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city (P-value=0.0000263).

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that dog owners in the country (sample 2) spend more time walking their dogs than do dog owners in the city (sample 1).

Then, the null and alternative hypothesis are:

\(H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0\)

The significance level is 0.05.

The sample 1, of size n1=20 has a mean of 10 and a standard deviation of 3.

The sample 2, of size n2=21 has a mean of 15 and a standard deviation of 4.

The difference between sample means is Md=-5.

\(M_d=M_1-M_2=10-15=-5\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{20}+\dfrac{4^2}{21}}\\\\\\s_{M_d}=\sqrt{0.45+0.762}=\sqrt{1.212}=1.101\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-5-0}{1.101}=\dfrac{-5}{1.101}=-4.54\)

The degrees of freedom for this test are:

\(df=n_1+n_2-1=20+21-2=39\)

This test is a left-tailed test, with 39 degrees of freedom and t=-4.54, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t<-4.54)=0.0000263\)

As the P-value (0.0000263) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city.

Using the t-distribution, it is found that since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.

At the null hypothesis, we test if dog owners in the country and in the city spend the same amount of time walking their dogs, that is:

\(H_0: \mu_{Co} - \mu_{Ci} = 0\)

At the alternative hypothesis, we test if dog owners in the country spend more time, that is:

\(H_1: \mu_{Co} - \mu_{Ci} > 0\)

The standard errors are:

\(s_{Co} = \frac{4}{\sqrt{21}} = 0.8729\)

\(s_{Ci} = \frac{3}{\sqrt{20}} = 0.6708\)

The distribution of the differences has:

\(\overline{x} = \mu_{Co} - \mu_{Ci} = 15 - 10 = 5\)

\(s = \sqrt{s_{Co}^2 + s_{Ci}^2} = \sqrt{0.8729^2 + 0.6708^2} = 1.1009\)

We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu\) is the value tested at the null hypothesis, for this problem \(\mu = 0\), hence:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{5 - 0}{1.1009}\)

\(t = 4.54\)

Since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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The value of side TS is,

⇒ TS = 28

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Additionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK

LY = HJ,

so, LY = 14

And, 42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

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Answer:

\(m\angle 3=30^\circ,~m\angle 8=150^\circ\)

Step-by-step explanation:

Angles and Lines

We must recall some properties of angles and lines:

Linear pair of angles: Two angles are linear if they are adjacent angles formed by two intersecting lines. They must add up to 180°.

Corresponding angles: They are angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are congruent, i.e., they have the same measure.

The figure shows two parallel lines a and b, crossed by the line m. These conditions make the following relations be true:

Angles 3 and 4 are linear pair

Angles 8 and 4 are corresponding.

The first relation leads to:

\(m\angle 3+m\angle 4 = 180^\circ\)

The second relation leads to:

\(m\angle 4 = m\angle 8\)

Since:

\(m\angle 3=x\)

\(m\angle 8=5x\)

Substituting:

\(x + 5x = 180^\circ\)

Simplifying:

\(6x = 180^\circ\)

Solving for x:

\(x = 180^\circ/6\)

\(x = 30^\circ\)

Now,

\(m\angle 3=x=30^\circ\)

\(m\angle 8=5x=150^\circ\)

\(m\angle 3=30^\circ,~m\angle 8=150^\circ\)

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

Answer: Points P, M, F, and C are coplanar.

Step-by-step explanation:

Answer: Total expenses if 3 widgets are produced is $11,018.00

Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000

E = 6.00 (3) + 11,000

E = 18.00 + 11,000

E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.

The ratio is 3:4:5.

Cosine by definition, is adjacent divided by hypotenuse, meaning that the value of the hypotenuse is 5. Then, we are given two other sides that are adjacent to angles A and B, which are 4 and 3 respectively.

This means that there are side lengths 3, 4, and 5, meaning that the ratio of the sides are 3:4:5.

Hope this helps.

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Answer:

D. Starla and Lewis will have the same balance in their accounts after 7 months.

Answer: 1800 feet

Step-by-step explanation:

Distance around baseball Diamond:

90 feet x 4 bases = 360 feet

360 feet x 5 batters who hit home runs = 1800 feet in total

Answer:

m‹EFG = m‹EFH + m‹HFG

• substitute:

\(130 \degree = 86 \degree + m \angle HFG \\ \\ m \angle HFG = 130 \degree - 86 \degree \\ \\ { \boxed{ \: \: m \angle HFG = 44 \degree}}\)

Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

\(=2x+h-2\)

Step-by-step explanation:

When want to simplify:

\(\frac{f(x+h)-f(x)}{h}\text{ given } f(x)=x^2-2x\)

So, let's substitute (x+h) into our f(x). This yields:

\(f(x+h)=(x+h)^2-2(x+h)\)

Substitute this and f(x) into our above expression to obtain:

\(=\frac{(x+h)^2-2(x+h)-(x^2-2x)}{h}\)

Simplify. First, square the first term:

\(=\frac{(x^2+2xh+h^2)-2(x+h)-(x^2-2x)}{h}\)

Distribute the -2 for the second term:

\(=\frac{(x^2+2xh+h^2)-2x-2h-(x^2-2x)}{h}\)

And distribute the negative for the last term:

\(=\frac{(x^2+2xh+h^2)-2x-2h-x^2+2x}{h}\)

Combine like terms:

\(=\frac{(x^2-x^2)+(-2x+2x)+(2xh+h^2-2h)}{h}\)

The first two expressions will cancel. This leaves us with:

\(=\frac{2xh+h^2-2h}{h}\)

Factor out an h:

\(=\frac{h(2x+h-2)}{h}\)

We can cancel the h. So, our final solution is:

\(=2x+h-2\)

And we're done!

Answer: 2-i

Step-by-step explanation:

multiply the fraction by 3-i/3-i

Answer:

The closet equivalent of the ratio of 'a' to 'c' is:

\(\frac{a}{c}=1.680\:\)

Step-by-step explanation:

Given

i.e.

a=0.63x

i.e.

c=3/8x

Hence,

\(\frac{a}{c}=\frac{0.63x}{\frac{3}{8}x}\)

\(\frac{a}{c}=1.680\:\)

Thus, the closet equivalent of the ratio of 'a' to 'c' is:

\(\frac{a}{c}=1.680\:\)

Dave and Frank are both right.

The correct answer would be Frank because 12 is less than 15.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Frank ate 12 pieces of pizza and Dave ate 15 pieces. “I ate 1/4 more,” said Dave. “I ate 1/5 less,” said Frank.

Therefore, If Dave ate ¼ more than Frank, we would need to divide the denominator by the amount of pizzas,

Thus, if 12÷4 is 3 he ate three more pizzas than Frank.

If we do the same for Frank, ⅕

15÷5=3

Hence, the correct answer would be Frank because 12 is less than 15.

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The expected rate of inflation is 0.068627 or 6.86%.

Real Rate of return:

The real rate of return defines the actual amount of return earned by an investment. Inflation reduces the real rate of return, so investor tries to invest in securities that could fetch more return than inflation.

The general formula of the inflation rate is:

\(IR=\frac{1+R_1}{1+R_2} -1\)

Given information is that

Nominal rate of return(R1)=9%

Real rate of return(R2)=2%

Now substitute these values in the above formula:

\(IR=\frac{1+R_1}{1+R_2} -1\\\\IR=\frac{1+0.09}{1+0.02} -1\)

IR=1.068627-1

IR=0.068627 or 6.86%

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Answer:

3 inches by 1 inches or 6 inches by 2 inches. Both answera are correct

Step-by-step explanation:

just an equivalent ratio

hope this helps can I get brainliest

Step-by-step explanation:

step 1. an ordered pair is enclosed in parenthesis.

step 2. (3, 5, 0) is an ordered pair.

Ordered pairs are representation of x and y values

None of the options is a ordered pair

The rules of valid ordered pairs are:

From the list of given options, none of the options obey all the above rules.

Hence, none of the options is a ordered pair

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Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer: $4

Step-by-step explanation:

In this situation let's set up a proportional relationship .

\(\frac{0.20}{x } = \frac{0.5}{10}\)     Now solve by cross multiply  

0.5x  = 2      Divide both sides by 0.5  

x = 4  

This means that if Emily bikes 10 miles, her mother will donate $4.

Answer:

\(\$4\)

Step-by-step explanation:

Number of \(0.5\) miles in \(10\) miles = \(10\)÷\(0.5\)

= \(20\)

Amount of money donated = \(0.20\) × \(20\)

= 4

\(\therefore\) Emily's mother donated a total of \(\$4\) given that Emily biked for 10 miles.

Hope this helps :)

The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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Answer:

\(6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24\)

B is the correct answer.

Answer:

calculator gave me 6.5732

Step-by-step explanation:

Answer:

Interest = $1.75

Step-by-step explanation:

Maria invest $600, and receives interest of $30 per year

We know that PRT/100= INTEREST

R=( 100*INTEREST)/(PT)

R = (100*30)/(600*1)

R= 3000/600

R= 5%

Jane invest $350 at Sam rate with Maria , that is 5% , for a year, her interest

Interest= 350*5*1/100

Interest = $1.75

Answer:

Step-by-step explanation:

The number of boxes of pies that the Chess Club must sell to reach their goal of $150 can be represented by the variable x. We can create the following equation to represent this relationship:

1.25x + 16.25 = 150

To find the number of boxes of pies that the Chess Club must sell, we can solve this equation by subtracting 16.25 from both sides and then dividing both sides by 1.25:

1.25x = 150 - 16.25

1.25x = 133.75

x = 133.75 / 1.25

x = 107.

Therefore, the Chess Club must sell 107 more boxes of pies to reach their goal of $150.

The time that the ball traveled is given as follows:

1.5 seconds.

The quadratic function determining the ball's height after t seconds is given as follows:

H(t) = -16t² + 24t.

The roots of the quadratic function in this problem are given as follows:

-16t² + 24t = 0.

16t² - 24t = 0

8t(2t - 3) = 0.

Hence we apply the factor theorem as follows:

Hence the time is given as follows:

1.5 - 0 = 1.5 seconds.

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Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-2*x-(6)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-2x-6 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.