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kompoz [17]
1 year ago
12

Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to

its resting place, the cheetah travels an average of 70 mph. If the cheetah traveled for 15 minutes, how many minutes did the return trip take to the nearest minute and second?
Set up the table as follows. Label the rows “To the River” and “From the River.” Label the columns “Distance,” “Rate,” and “Time (in Hours).” Let t represent the unknown quantity in the problem. Fill in the table.
Mathematics
1 answer:
Eduardwww [97]1 year ago
3 0

Answer:

9.55 minutes

Step-by-step explanation:

x hours to go to the river

0.25-x hours to come back, since 15 minutes is 0.25 hr.

to the river 40 mph * x hours =40x miles

from the river 70 mph (0.25-x) hours=17.5-70x

those two are equal

40x=17.5-70x

110x=17.5

x=17.5/110=0.159 hours

9.55 minutes

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The table shows the ratio between the number of books ordered and their cost: Find equivalent ratios when the number of books or
Nana76 [90]

Answer:

The answer is below

Step-by-step explanation:

The table shows the ratio between the number of books ordered and their cost: Number of Books Cost (dollars) 7 21 8 24 9 27 Find equivalent ratios when the number of books ordered is 1, 2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin, explain how to plot the three equivalent ratios on a coordinate grid.

Answer: Let the number of books be represented as x and the cost (dollars) be represented as y. From the table the ordered pairs in the form (x, y) can be gotten. (7, 21), (8, 24), (9, 27). To get the relationship between the number of books and the cost, we can use the formula of a straight line.

Using point (7, 21) and (8, 24):

y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-21=\frac{24-21}{8-7}(x-7)\\ \\y-21=3(x-7)\\\\y=3x-21+21\\\\y=3x

When the number of books ordered is 1, 2, 3 the following pairs are:

For x = 1.     y = 3x = 3(1) = 3

For x = 2     y=3x = 3(2) = 6

For x = 3     y = 3x = 3(3) = 9

The ordered pairs are (1, 3), (2, 6), (3, 9)

The graph is attached

To plot the ordered pairs, the number of books are plotted on the x coordinate and the cost on the y coordinate  

8 0
2 years ago
Line WY is an altitude in triangle WXZ. If ΔYWZ ~ ΔYXW, what is true about XWZ? XWZ is an obtuse angle. XWZ is a right angle. XW
topjm [15]
<span>In triangle WXZ,

Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
</span><span>If ΔYWZ ~ ΔYXW
</span>∠WXY = ∠WZY
<span>
Then, we can also conclude 
</span>∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)

Now, in any triangle, the sum of all the three angles is 180.

In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°

Similarly, in WZY.

Hence, we conclude that XWZ is a right angle.

7 0
2 years ago
Read 2 more answers
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.
ollegr [7]

Answer: a. A point estimate for p is 0.597 .

b. The 95% confidence interval for p.

Lower limit = 0.48

Upper limit = 0.71

Step-by-step explanation:

Given : Sample size of professional actors : n= 67

Number of extroverts : x= 40

Let p represent the proportion of all actors who are extroverts.

a. The point estimate for p = sample proportion = \hat{p}=\dfrac{x}{n}

=\dfrac{40}{67}=0.597

b. Confidence interval for population proportion :

\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

Since the critical value for 95% confidence interval is 1.96 , so the 95% confidence interval for p would be

0.597\pm (1.96)\sqrt{\dfrac{0.597(1-0.597)}{67}}

0.597\pm (1.96)\sqrt{0.0036}

0.597\pm (1.96)(0.06)

0.597\pm 0.1176

(0.597-0.1176,\ 0.597+0.1176)\\\\=(0.4794,\ 0.7146)\\\\\approx(0.48,\ 0.71)

In the 95% confidence interval for p.

Lower limit = 0.48

Upper limit = 0.71

8 0
2 years ago
Read 2 more answers
1. WHEELS Zack is designing wheels for a concept car.
mars1129 [50]

Answer:

9 inches

Step-by-step explanation:

Diameter=D

Radius=R

D=(2)R

(18)=(2)R

18/2=2/2 R

9=R

4 0
2 years ago
the equation y equals 1/5x represents a proportional relationship. explain how you can tell the relationship is proportional fro
Allisa [31]
If the equation is in y = k*x form, then we have a direct proportional relationship between x and y. In this case, y = (1/5)*x is in the form y = k*x where k = 1/5. So this equation is proportional. The constant of proportionality is k = 1/5

In terms of a graph, you can tell if it has the following properties:
1) The graph goes through the origin (0,0) which is where the x and y axis cross
2) The graph is a straight line

You should find that graphing y = (1/5)x will satisfy both properties above, so that will visually confirm you have the right answer. The graph is shown in the attached image. The red line represents the graph of the equation. The red line goes through (0,0) and (5,1), which are point A and point B respectively.

8 0
2 years ago
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