Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?



Enter the exact answer.
Hint: The distance formula is that distance = rate * time, so for example in one and a half hours, Ben has walked 3 * 1.5 miles.

Amanda catches up to Ben in ____________ hours.

Answer:

the second option : ST and WX

Step-by-step explanation:

congruent means they would completely cover each other when oriented in the same direction and positioned at the same location.

after dying the two mirroring actions we get

VS correlates to ZW

ST correlates to WX

TU correlates to XY

UV correlates to ZY

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Answer:

Step-by-step explanation:

Of the items sold, sodas were 2/(2+1) = 2/3 of the total.

  (2/3)(228) = 152 . . . sodas were sold

  152/2 = 76 . . . . hot dogs were sold

Hello!

[tex]\large\boxed{(x + 2)(x + 3)}[/tex]

x² + 5x + 6

Find two numbers that add up to 5 and multiply to 6. We get:

2, 3

Therefore:

(x + 2)(x + 3)

Answer:

0.7

Step-by-step explanation:

67/10 is the same as 6.7 when you subtract the 0.7 you will remain with 6

Answer:

6/7

Step-by-step explanation:

7 days make a week. 7 would go into the denominator and 6 would go in the numerator. 6 is the amount of days through the week that it is dry.

Answer:

6/7

Step-by-step explanation:

[tex]\frac{number \ of \ dry \ days}{total \ number \ of \ days \ in \ a \ week} =\frac{6}{7}[/tex]

Step-by-step explanation:

2tan 30° / 1 + tan² 30° =

2(⅓√3) /1 + (⅓√3)² =

⅔√3 / 1+ ⅓ =

⅔√3 / 4/3 =

2/4 √3 =

½√3 = sin 60° (proven)

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Answer:

  2√13

Step-by-step explanation:

The distance between the center of the circle and a point on the circle is the radius. That distance is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((-5 -1)² +(6 -2)²) = √(36 +16) = √52

  d = 2√13

The radius of the circle is 2√13.

Answer:

-18

Step-by-step explanation:

B=-6 C=2 P.E.M.D.A.S.

b - 6(c)

-6 - 6(2)

-6 - 12 . The negatives cancel out, adding each other

-6 + -12

= -18 :)

Answer:

b - 6c

= -6 - 6x2

= -6 x( 1+2)

= -6x3

= -18

Answer:

[tex]Pr= 0.00725[/tex]

Step-by-step explanation:

Given

[tex]p = 0.05[/tex] ---- probability that each component fails

[tex]n = 3[/tex]

Required

[tex]P(System\ Overheats)[/tex]

We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

The events that the system will overheat are: xyz', xy'z, x'yz and xyz

Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)

So, we have:

[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]

[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]

[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]

[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]

So, the required probability is:

[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]

[tex]Pr= 0.00725[/tex]

Answer:

0.015 and 3/200.

Step-by-step explanation:

1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.

0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.

Answer:

C. -4

Step-by-step explanation:

Answer:

(c) - 4

is your right answer

Answer:

The expected number of winning balls that Heather draws is 0.3.

Step-by-step explanation:

The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Expected value of the hypergeometric distribution:

The expected value is given by:

[tex]E(X) = \frac{nk}{N}[/tex]

Expected number of blue and green balls:

40 balls, which means that [tex]N = 40[/tex]

2 are chosen, which means that [tex]n = 2[/tex]

25 are blue, which means that [tex]k = 25[/tex]

So

[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]

1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.

Of the blue balls, 12% are winning.

Of the green balls, 20% are winning.

Calculate the expected number of winning balls that Heather draws.

[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]

The expected number of winning balls that Heather draws is 0.3.

Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

∴

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

Answer:

y = 5/4 x - 23/4

Step-by-step explanation:

4x + 5y = 31

5y = - 4x +31

y = -4/5 x + 31/5

⊥ slope = 5/4

-7 = 5/4 (-1) + B

-28 = -5 + 4b

-23 = 4B

b = -23/4

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Answer:

  ∠4

Step-by-step explanation:

"Alternate" means the angle is on the other side of the transversal t. "Exterior" means it is on the outside of line e crossing the transversal. The alternate exterior angle to angle 8 is angle 4.

Answer:

Yes it is very good for establishing identities.

Step-by-step explanation:

Since its a very preferable start it is a very good way to establish identity.

Answer:

Place the event

But he sobered down when he saw that Jimmy was wounded.

Jimmy comes

up with the plan of curing the Emperor by telling him to eat watermelon.

The Emperor fa

lls sick with dysentery, which has plagued the kingdom.

The Emperor is cured after eating a few slices of fresh watermelon.

The next day, the page asks the Emperor t

o consume a slice of watermelon as a cure.

↓

↓

Reset Submit

Step-by-step explanation:

Answer:

1984

Step-by-step explanation:

Hi there!

[tex]\large\boxed{f(9) = 12}[/tex]

Evaluating f(x) at x = 9 means we must use the piecewise function where x = 9 is included.

f(x) = 12 includes 9 because a "≤" is inclusive of the interval. Thus:

f(9) = 12

Step-by-step explanation:

ΔABC, where AB = 8 cm, BC = 6 cm, B = 70° Construction: (i) Draw the ∆ABC with the given measurements. (ii) Construct the perpendicular bisector at any two sides (AB and BC) and let them meet at S which is the circumcircle. (iii) S as centre and SA = SB = SC as radius, draw the circumcircle to pass through A, B, and C. Circum radius = 4.3cm .draw-triangle-abc-where-cm-bc-and-70-and-locate-its-circumcentre-and-draw-the-circumcircle

Answer:

It is A and B

Step-by-step explanation:

Answer:

I guess the question is incomplete

Answer:

[tex]\sum_{n = 1}^{7} -2 -2n[/tex]

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference of consecutive terms is always the same, called common difference.

The nth term of a sequence is given by:

[tex]a_{n} = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term and d is the common difference.

Sigma notation to represent the sum of the first seven terms

Sum going from the index starting at 1 and finishing at 7, that is:

[tex]\sum_{n = 1}^{7} f(n)[/tex]

Now we have to fund the function, which is given by an arithmetic sequence.

−4, −6, −8,

First term -4, common difference - 6 - (-4) = -6 + 4 = -2, so [tex]a_1 = -4, d = -2[/tex]

Then

[tex]f(n) = a_{n} = a_1 + (n-1)d[/tex]

[tex]f(n) = -4 + (n-1)(-2)[/tex]

[tex]f(n) = -4 - 2n + 2 = -2 - 2n[/tex]

Sigma notation:

Replacing f(n)

[tex]\sum_{n = 1}^{7} -2 -2n[/tex]

Answer:

Pvalue = 0.1505

y = 0.550x1 + 3.600x2 + 7.300

Step-by-step explanation:

Given the data :

Study Hours GPA ACT Score

5 4 27

5 2 18

5 3 18

1 3 20

2 4 21

Using technology, the Pvalue obtained using the Fratio :

F = MSregression / MSresidual = 30.228571/ 8.190476 = 3.69

The Pvalue for the regression equation is:

Using the Pvalue from Fratio calculator :

F(1, 3), 3.69 = 0.1505

Using the Pvalue approach :

At α = 0.01

Pvalue > α ; Hence, we fail to reject H0 and conclude that ; There is not enough evidence to show that the relationship is statistically significant.

The regression equation :

y = A1x1 + A2x2 +... AnXn

y = 0.550x1 + 3.600x2 + 7.300

x1 and x2 are the predictor variables ;

y = predicted variable

You'll need 2 more lines to complete this two column proof.

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

Line 4

For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

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

Line 5

The statement is what you want to prove since this is the last line.

So the statement is [tex]p || q[/tex]

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Answer:

What function?

Step-by-step explanation:

Answer:

The answer is

x equal -243

Answer:

-243 is yr correct answer.

Step-by-step explanation:

hope it helps

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Answer:

  88 ounces

Step-by-step explanation:

Let x represent the number of ounces of the less expensive alloy in the mix. Then the cost of the mix will be ...

  6.75x +10(55) = 8(55+x)

  110 = 1.25x . . . . . . subtract 440+6.75x

  88 = x . . . . . . . . divide by 1.25

88 ounces of $6.75/oz silver must be used.

Answer:

Step-by-step explanation:

1. subtract 3.5-3.5 and 12.5-3.5

2.You should 4t=9

3. Divide 4 ÷ 4 and 9 ÷ 4

4. You should have t = 2.25

Answer:

t = 2.25

Step-by-step explanation:

Step 1 :- Divide both side by 3.5.

Step 2 :- Divide each side by 4.