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Bingel [31]
2 years ago
8

You can perform 4 push-ups in 24 seconds. Write an equation that represents the relationship between time x and the number of pu

sh-ups y.
Mathematics
1 answer:
Yuki888 [10]2 years ago
5 0
Y= 1/6x is the answer because 4/24 is 1/6
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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= root 2 cm.
Nata [24]

Given CD is an altitude such that AD=BC , AB=3 cm and CD= √2 cm.

Let AD=x, Since given AB=3

                                     AD+DB=3

                                       x+DB = 3

                                        DB = 3-x

Since ΔBCD is rght angle triangle, let's apply Pythagoras theorem

BC^{2} = DB^{2} +CD^{2}

BC^{2} = (3-x)^{2} +(\sqrt{2} )^{2}

BC^{2} =(3-x)^{2} +2

Since given AD=BC,let us plugin BC=x in above step.

x^{2} =(3-x)^{2} +2

x^{2} =9-6x+x^{2} +2

6x=11

x=\frac{11}{6}

Now we know AD=x=\frac{11}{6} and given CD=√2.

Let us apply Pythagoras theorem for ΔACD

AC^{2} =AD^{2} +DC^{2}

AC^{2} = (\frac{11}{6} )^{2} +(\sqrt{2} )^{2}

AC^{2} =\frac{193}{36}

AC=\sqrt{\frac{193}{36} } = 2.315cm

3 0
3 years ago
A recent Gallup poll found that 36% of U.S. teens aged from 13 to 17 years old have a computer with [(6)] Internet access in the
In-s [12.5K]

Answer:

Step-by-step explanation:

a) The population parameter is the population proportion.

b) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 1028

p = 36/100 = 0.36

q = 1 - 0.36 = 0.64

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.99 = 0.1

α/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.995

The z score corresponding to the area on the z table is 2.58. Thus, confidence level of 99% is 2.58

Therefore, the 99% confidence interval is

0.36 ± 2.58 × √(0.36)(0.64)/1028

The lower limit of the confidence interval is

0.36 - 0.039 = 0.321

The upper limit of the confidence interval is

0.36 + 0.039 = 0.399

Therefore, with 99% confidence interval, the proportion of U.S. teens aged from 13 to 17 years old that have a computer with Internet access in their rooms is between 0.321 and 0.399

c) for a margin of error of 1%, that is 1/100 = 0.01, then

0.01 = 2.58 × √(0.36)(0.64)/n

0.01/2.58 = √0.2304/n

0.00387596899 = √0.2304/n

Square both sides

0.00001502314 = 0.2304/n

n = 0.2304/0.00001502314

n = 15336

5 0
3 years ago
Suppose that a box of 86 circuits is sent to a manufacturing plant. Of the 86 circuits shipped, 5 are defective. The plant manag
Triss [41]

Answer:

the probability that the shipment is accepted is 0.8865

Step-by-step explanation:

Given the data in the question;

N = 86,  n/d = 5 and n = 2

now, without replacement

the probability that the shipment is accepted will be;

probability that the shipment is accepted = probability that non is defectives

so p( non is defective ) = ( (86-5)/86) × ((86-5-1)/(86-1))            

p( non is defective ) =  ( 81 / 86) × (80/85)

p( non is defective ) =  0.8865

Therefore, the probability that the shipment is accepted is 0.8865

7 0
2 years ago
WILL MARK BRAINLIEST
sp2606 [1]

To make this new triangle I am going to pretend that the original triangle was at the points (4,4) (-4,4) and (0,8). So if this was dilated down by 1/2 then the triangles points would be (2,2) (-2,2) and (0,4). Then if it is reflected over the x-axis the new points would be (2,-2) (-2,-2) and (0,-4) and if it was translated left by 2 units then the points would be (0,-2) (-4,-2) and (-2, -4), then if the triangle was translated up by 4 units the points and the new triangle would be (0,2) (-4,2) and (-2,0). And that would be what the new triangle would be.

The triangle went from (4,4) (-4,4) and (0,8) to (0,2) (-4,2) and (-2,0).

7 0
3 years ago
Five less than twice what negative number squared is 157?
fenix001 [56]
Five less than twice what negative number squared is 157 <- put into an expression
-5 + 2(-x^2) = 157
Now simplify:
-5 + -2x^2 = 157
-2x^2 = 162
-2x^2 - 162 = 0
2x^2 + 162 = 0
x^2 + 81 = 0

3 0
3 years ago
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