During a mathematics test, 18 students answered question 1 correctly, 23 students answered question 2 correctly, 8 students got them both correct and 11 students answered incorrectly on both questions. How many students took the test?(A) 41 (B) 44 (C) 49 (D) 52 (E) 60

Answer:

A. 549.5

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

2x+6=18

2x=12

x=6

Step-by-step explanation:

2(x+3)=18

x+3=18÷2

x+3=9

x=9-3

x=6

2x+15=27-4x

2x+4x=27-15

6x=12

x=12÷6

x=2

Answer:

[tex](a)\ Pr = 0.25[/tex]

[tex](b)\ Pr = 0.50[/tex]

Step-by-step explanation:

Given

[tex]Flips = 4[/tex]

First, we calculate the sample size;

The coin has two possible outcomes (i.e. head or tail) and the number of flips is 4.

So, the sample size (N) is:

[tex]N = 2^4[/tex]

[tex]N = 16[/tex]

Solving (a): Probability the outcome of the first and last flip is head.

The possible outcomes for this event are:

[tex]n = \{(HHHH), (HHTH), (HTHH),(HTTH)\}[/tex]

[tex]n(n) = 4[/tex]

The probability is:

[tex]Pr = \frac{n(n)}{N}[/tex]

[tex]Pr = \frac{4}{16}[/tex]

[tex]Pr = 0.25[/tex]

Solving (a): Probability that the outcome of at least 2 consecutive flips is head.

The possible outcomes for this event are:

[tex]n = \{(HHHH), (HHHT),(HHTH), (HTHH),(THHH),(TTHH),(HHTT), (THHT)\}[/tex]

[tex]n(n) = 8[/tex]

The probability is:

[tex]Pr = \frac{n(n)}{N}[/tex]

[tex]Pr = \frac{8}{16}[/tex]

[tex]Pr = 0.50[/tex]

Answer:

Step-by-step explanation:

x-2=24          x=26

Answer:  13+18i

Step-by-step explanation:

(4-i)(2+5i)

8+20i-2i-5(i)^2

as we know that  i^2=-1

8+18i-5(-1)

8+18i+5

13+18i

Answer:

Ban has 9,000

Michel has 27,000

Bob has 36,000

Step-by-step explanation:

BA: MI: BO

1: 3: 4 (1+3+4 = total number)

BA:  [tex]\frac{1}{8}[/tex] of 72,000 (72,000 ÷ 8 x 1) = 9,000

MI: [tex]\frac{3}{8}[/tex] of 72,000 (72,000 ÷ 8 x 3) = 27,000

BO: [tex]\frac{4}{8}[/tex] of 72,000 (72,000 ÷ 8 x 4) = 36,000

Answer:

Step-by-step explanation:

For this equation: a=3, b=4, c=2

3x2+4x+2=0

Step 1: Use quadratic formula with a=3, b=4, c=2.

x= −b±√b2−4ac / 2a

x= −(4)±√(4)2−4(3)(2)  /  2(3)

x= −4±√−8  /  6

Answer:

No real solutions.

The quadratic equation 3x² + 4x + 2 = 0 does not have a real solution.

Quadratic equations are second degree polynomial equations which is of the form ax² + bx + c = 0, where a, b and c are integers.

Given quadratic equation is,

3x² + 4x + 2 = 0

Quadratic formula to find the solution is,

x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] /  2a, where [tex]\sqrt{b^2-4ac}[/tex] is called discriminant.

Here, a = 3, b = 4 and c = 2

Substituting,

x = [-4 ± [tex]\sqrt{4^2-(4*3*2)}[/tex]] /  (2 × 3)

  = [-4 ± √(16 - 24)] / 6

  = [-4 ± √(-8)] / 6

This has no real solution since the value inside the discriminant is negative.

Hence the quadratic equation has no real solution.

Learn more about quadratic Equations here :

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Answer:

130

Step-by-step explanation:

3*10 =30+100=130

Answer:

Volume is 60ft³

Step-by-step explanation:

b²h/3

b=6

h=5

The volume of a square-based pyramid will be 180 ft³. Option D is correct.

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is the same as its base, then its volume is:

[tex]\rm V = B^2 \times h \\\ V = 6^2 ft \times 5 \ ft \\\ V=180 \ ft^2[/tex]

Learn more about the volume of a prism refer:

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Answer:

[tex]y = 1[/tex]

Step-by-step explanation:

[tex] \frac{3}{39} = \frac{y}{13} [/tex]

Cross multiply

[tex]39 = 39y[/tex]

Divide by 39

[tex]y = 1[/tex]

Answer:

[tex]\boxed {\boxed {\sf y=1}}[/tex]

Step-by-step explanation:

To solve the proportion, we must solve for the variable. This is done by isolating the variable.

[tex]\frac {3}{39}= \frac {y}{13}[/tex]

The variable, y, is being divided by 13. The inverse of division is multiplication. Multiply both sides of the proportion by 13.

[tex]13*\frac {3}{39}= \frac {y}{13}*13[/tex]

[tex]13*\frac {3}{39}=y\\1=y[/tex]

Another way to solve is by cross multiplying. Multiply the 1st numerator by the 2nd denominator, then the 1st denominator and the 2nd numerator.

[tex]\frac {3}{39}= \frac {y}{13}[/tex]

[tex]3*13=39*y\\39=39y[/tex]

Divide both sides by 39 to isolate the variable.

[tex]39/39=39y/39 \\1=y[/tex]

In this proportion, y is equal to 1.

Answer:

a) 0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.

b) 0.9463 = 94.63% probability that Jodi will score 77% or lower.

c) 400 questions.

d) Yes, because the formula is the same, independently of the value of p.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.81[/tex]

Question a:

100 questions means that [tex]n = 100[/tex]

For the approximation, we have that:

[tex]\mu = p = 0.81[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{100}} = 0.0392[/tex]

This probability is the pvalue of Z when X = 0.77. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.77 - 0.81}{0.0392}[/tex]

[tex]Z = 1.02[/tex]

[tex]Z = 1.02[/tex] has a pvalue of 0.8461

0.8461 = 84.61% probability that Jodi scores 77% or lower on a 100-question test.

Question b:

Now [tex]n = 250[/tex], so:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.81*0.19}{250}} = 0.0248[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.77 - 0.81}{0.0248}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463

0.9463 = 94.63% probability that Jodi will score 77% or lower.

Question c:

The formula for the standard deviation is:

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Meaning that it is inversely proportional to the square root of the sample size.

So, to reduce the standard deviation by half, the number of question must be multiplied by (2)^2 = 4.

100*4 = 400

So 400 questions.

d. Laura is a weaker student for whom p = 0.76. Does the answer you gave in (c) for standard deviation of Jodi's score apply to Laura's standard deviation also?

Yes, because the formula is the same, independently of the value of p.

Answer:

7

Step-by-step explanation:

13-6=7 compare maybe.....

Answer:

120 feet is the answer

Answer:

Answer is 64.

Step-by-step explanation:

524288/8192 = 64

Answer:

1500 millimeters

Step-by-step explanation:

1 meter = 1000 millimeters

1.5 meters = 1500 millimeters

Answer:

24

Step-by-step explanation:

Its just  1/2 6x8=24.

its like 6x8=48 and half of it is 24

Answer:

9

Step-by-step explanation:

9

9x9 = 81

Therefore, 81 ÷ 9 is 9

Answer:

-3,4

Step-by-step explanation:

just follow up the other coordinates

Answer:

option E is your correct answer

mark as brainliest

Answer:

C. 10

Step-by-step explanation:

AC = 4 units

BC = 5 units

use the triangle formula

1/2 × 4 × 5 = 10

Answer:

the answer is 52 Lions

Step-by-step explanation:

I think that's the answer if I'm wrong please tell me if I'm wrongI can ask the people who are around me.

Answer:

82

Step-by-step explanation:

Answer:

instructions??????????

Answer:

X = 6

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

Since there are a total of 30 chips and 10 yellow ones, you have to divide then convert them into a fraction.

10/30 = 1/3

I don't what form of measurement to use (like grams, cusp, etc.) but I'm pretty sure it'd be cups

I think it's 5/96 or .05208333

So, 5/8 is .625. Dividing that up in throwing it into 12 cupcakes.

Answer:

c=7.180 miles. 2. Jack is on one side of a 200-foot-wide canyon and Jill is on the other. Jack and Jill can both ... a=2.947 miles. 5. Airplane A is flying directly toward the airport which is 20 miles away. The pilot notices ...

Answer:

y=45° x=81°

Step-by-step explanation:

the 2 angles across the outside angles sum up to the given number so just subtract 95-50= 45, with that we know subtract from the total sum of every triangle which is 180. So we add the 2 angles we have now, 50+45=99. Now we subtract, 180-99= 81.