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2 years ago

Answer both questions thanks

Mathematics

1 answer:

horrorfan [7]2 years ago

8 0

Answer:

See below, please.

Step-by-step explanation:

1. (a) 9/24 = 0.375 = 37.5% (multiply by 100 and put a % sign on the end)

(b) 60% = 'x' karats

0.60 = x/24

x = (0.60)(24) = 14.4 karats

2. (a) 2g 10-karat gold + 2g 14-karat gold

= (2g * 10/24) + (2g * 14/24) = (20/24 + 28/24)g = (48/24)g = 2g Gold in a 4-gram alloy, so it is 50% gold

(b) 6g 24-karat gold + 4g 9-karat gold

= (6g * 24/24) + (4g * 9/24) = (144/24 + 36/24)g = (180/24)g = 7.5g Gold in a 10-gram alloy, so it is 75% gold

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Suppose we have 3 cards identical in form except that both sides of the first card are colored red, both sides of the second car

Nikolay [14]

Answer:

probability that the other side is colored black if the upper side of the chosen card is colored red = 1/3

Step-by-step explanation:

First of all;

Let B1 be the event that the card with two red sides is selected

Let B2 be the event that the

card with two black sides is selected

Let B3 be the event that the card with one red side and one black side is

selected

Let A be the event that the upper side of the selected card (when put down on the ground)

is red.

Now, from the question;

P(B3) = ⅓

P(A|B3) = ½

P(B1) = ⅓

P(A|B1) = 1

P(B2) = ⅓

P(A|B2)) = 0

(P(B3) = ⅓

P(A|B3) = ½

Now, we want to find the probability that the other side is colored black if the upper side of the chosen card is colored red. This probability is; P(B3|A). Thus, from the Bayes’ formula, it follows that;

Thus;

P(B3|A) = [⅓×½]/[(⅓×1) + (⅓•0) + (⅓×½)]

P(B3|A) = (1/6)/(⅓ + 0 + 1/6)

P(B3|A) = (1/6)/(1/2)

P(B3|A) = 1/3

5 0

3 years ago

Rafael races his bicycle for

pychu [463]

Distance traveled = 70 m
Number of rotations = 29

We know, Circumference * Number of rotations = Distance traveled
So, C = 70 / 29
C = 2.41 m

Now, we know, diameter = C / π
So, d = 2.41/3.14 = 0.768

In short, Your Answer would be: 0.8 m

Hope this helps!

6 0

3 years ago

Read 2 more answers

What is the measure of EAB in circle F?<br> 72°<br> 92°<br> 148°<br> 200°

Arada [10]

We have been given a diagram. We are asked find the measure of arc EAB.

First of all, we will find the measure of arcs ED and CB using our given information.

We know that measure of an inscribed angle is half the measure of intercepted arc.

We can see that angle EBC is inscribed angle of arc EDC, so measure of arc EDC will be twice the measure of angle EBC.

$\widehat{EDC}=2\times m\angle EBC$

$\widehat{EDC}=2\times 80^{\circ}$

$\widehat{EDC}=160^{\circ}$

Similarly, we will find the measure of arc DCB.

$\widehat{DCB}=2\times m\angle DEB$

$\widehat{DCB}=2\times 70^{\circ}$

$\widehat{DCB}=140^{\circ}$

$\widehat{ED}=\widehat{EDC}-\wdiehat{DC}$

$\widehat{ED}=160^{\circ}-88^{\circ}$

$\widehat{ED}=72^{\circ}$

$\widehat{ED}+\widehat{DCB}+\widehat{EAB}=360^{\circ}$

$72^{\circ}+140^{\circ}+\widehat{EAB}=360^{\circ}$

$212^{\circ}+\widehat{EAB}=360^{\circ}$

$\widehat{EAB}=360^{\circ}-212^{\circ}$

$\widehat{EAB}=148^{\circ}$

Therefore, the measure of arc EAB is 148 degrees and option C is the correct choice.

8 0

3 years ago

Read 2 more answers

A marketing research company desires to know the mean consumption of milk per week among people over age 32. A sample of 440 peo

Softa [21]

Answer:

The 98% confidence interval for the mean consumption of milk among people over age 32 is between 3.3 and 3.5 liters.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.8}{\sqrt{440}} = 0.1$

The lower end of the interval is the sample mean subtracted by M. So it is 3.4 - 0.1 = 3.3 liters

The upper end of the interval is the sample mean added to M. So it is 3.4 + 0.1 = 3.5 liters

The 98% confidence interval for the mean consumption of milk among people over age 32 is between 3.3 and 3.5 liters.

7 0

2 years ago

If hj=7x-27 find the value of x

Harlamova29_29 [7]

Answer:

x=7

Step-by-step explanation:

HI + IJ = HJ

3x-5 + x-1 = 7x-27

Combine like terms

4x-6 = 7x-27

Subtract 4x from each side

4x-6 -4x= 7x-27-4x

-6 = 3x-27

Add 27 to each side

-6+27 = 3x-27+27

21 = 3x

Divide by 3

21/3 = 3x/3

7 =x

5 0

2 years ago