Learning Task No.2
A. Find the missing terms and write the rules.
1. 5,6,8,15
2. 18,20,24_38
3. 14, 17, 20,23,
4. 24, 30, 36, 42,
5. 1, 10, 100,​

Answer:

yes it does. good job on your A.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

b. (4×12)+(3×7)

48+21= 69

she spent $69

Answer:

Area of a circle= π r square

22/7 × 6 ×6

22/7×36

= 792/7

=113.40

Answer:

-5

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

-2 - 3 = -5

Check with the third term and the second term

-7 - (-2) = -7 +2 = -5

The common difference is -5

Answer:

[tex] a^{5} [/tex]

Step-by-step explanation:

Given the mathematical expression;

a⁸/a³

To rewrite the expression in the form [tex] a^{m} [/tex]

We would have to apply the law of indices.

[tex] Law \; of \; division = \frac {a^{x}}{a^{y}} = a^{x - y} [/tex]

[tex] Law \; of \; division = \frac {a^{8}}{a^{3}} = a^{8 - 3} [/tex]

[tex] a^{m} = a^{8 - 3} = a^{5} [/tex]

Answer:

2X2

Step-by-step explanation:

Answer: 10

Step-by-step explanation: 5 x 2 = 10

                                             5 + 5 = 10

Answer:

D. (-2, -11)

Step-by-step explanation:

Since -2 - 9 = -11, it fits into the equation x - 9 = y, with -2 being "x" and -11 being "y".

And out of all the options, D is the only one that works.

Answer:

A) - 0.8 Ibs

B) There isn't enough information

    The standard deviations of the difference scores is needed

Step-by-step explanation:

N = 110 female first year college students

Mean weight at beginning of study = 130.6 Ib

Mean weight after six ( 6 ) months = 131.4 Ib

standard deviation = 20 pounds

A) Determine the change in the mean weight over the six(6) months period

mean weight at beginning - mean weight after six(6) months

= 130.6 - 131.4

= -0.8 Ibs

B) Determine if there is sufficient information to find a confidence interval

There isn't sufficient information to determine the confidence interval but in other to determine the confidence interval or conduct an estimate You need standard deviations of the difference scores to calculate the standard error of mean

Answer:

Option D

Step-by-step explanation:

[tex]60+45+75=180[/tex]

[tex]Triangle ~has ~the~ sum ~of ~angle =180[/tex]

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hope it helps...

have a great day!!

Answer:

D will be your answer!!

Step-by-step explanation:

hope it helps

Answer:

x=10

Step-by-step explanation:

I guess solve for x

5x=50

x=10

Answer:

x=10

Step-by-step explanation:

Subtract to 25 from both sides

5x+25-25=75-25

so 75- 25 is 50

then ur left with 5x=50 so u divide because 5 is by x which means multipy so u do the opposite which is divding

5÷50 =10

Answer:

y

=

3

√

−

2

a

x

y

=

−

3

√

−

2

a

x

Step-by-step explanation:

Answer:

We know that:

If A is an even integer number, then A + 1 is an odd number

If B is an odd number, then B + 1 is an even number.

We also know that the product of two odd numbers is odd, and the product of two even numbers is even.

We want to prove that:

For all integers n, n^2 + n + 1 is odd.

We have two cases.

If n is even, then:

n^2  is the product of two even numbers, so is even.

n^2 + n is the sum of two even numbers, then it is even.

And:

(n^2 + n) + 1  is an even number plus one, so it is odd.

Now let's assume that n is odd.

n^2 is the product of two odd numbers, then n^2 is odd.

n^2 + n is the sum of two odd numbers, then it is even.

And similar as the previous case:

(n^2 + n) + 1 is an even number plus one, so it is odd.

Answer:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

Step-by-step explanation:

According to the statement, we have the following information about the lengths of the right triangle:

Hypotenuse

[tex]3\cdot x + 14[/tex]

Long leg

[tex]3\cdot x + 13[/tex]

Short leg

[tex]x[/tex]

By the Pythagoric Theorem, we have the following expression:

[tex](3\cdot x + 14)^{2} = x^{2} + (3\cdot x + 13)^{2}[/tex] (1)

[tex]9\cdot x^{2}+84\cdot x + 196 = x^{2} + 9\cdot x^{2} + 78\cdot x + 169[/tex]

[tex]9\cdot x^{2} + 84\cdot x + 196 = 10\cdot x^{2} + 78\cdot x +169[/tex]

[tex]x^{2} -6\cdot x -27 = 0[/tex]

[tex](x-9)\cdot (x+3) = 0[/tex]

As length is a positive variable by nature, then the only possible solution is [tex]x = 9[/tex]. Lastly, the side lengths of the right triangle are:

Hypotenuse: 41 meters, Long leg: 40 meters, Short leg: 9 meters.

Answer:

69.12

Step-by-step explanation:

12x5.76

Answer

69

Step-by-step explanation:

12×5.75=69

Answer:

Where are the statements?

Step-by-step explanation:

Where are the statements?

9514 1404 393

Answer:

  (c)  (0, 6)

Step-by-step explanation:

Conventionally, an "ordered pair" is a pair of items in parentheses, separated by a comma. The items don't have to be numbers. (0, 6) is an ordered pair.

__

Comments on the other answer choices

Curly braces are usually used as delimiters of a set, not an ordered pair.

Three items do not constitute a "pair." Rather, they are a "triple."

Items without any particular indicator of grouping are usually not considered a "pair."

Answer:

650,000 cm²

Step-by-step explanation:

10x6.5=65 METERS squared.  They want it in CENTIMETERS squared.

65m² = 650,000cm²

Answer:

32.5[tex]m^{2}[/tex]

Step-by-step explanation:

The coloured triangle with the blank triangle area =

(14m x 6.5m)÷2 = 45.5[tex]m^{2}[/tex]

The blank triangle area =

[(14-10m) x 6.5m]÷2 = 13[tex]m^{2}[/tex]

Therefore:

The coloured triangle area =

(45.5 - 13)[tex]m^{2}[/tex]

=32.5[tex]m^{2}[/tex]

Answer:

V = πr²h

V = 3.14 (5cm)²(7 cm)

V = 3.14 (25cm²) ( 7 cm)

V = 3.14 (175 cm³)

V = 549.50 cm³

Answer:

F(x) =2x+3

Step-by-step explanation:

F(x) =2x+3...............

Answer:

[tex]consider : (0, 3) \: and \: (1, 5) \\ gradient = \frac{5 - 3}{1 - 0} \\ = 2 \\ from : \: y = mx + c \\ consider \: (0, 3) \\ 3 = (2 \times 0) + c \\ c = 3 \\ therefore \: equation \: is : \\ y = 2x + 3[/tex]

Answer:

1.25 gallons of orange juice needed

Step-by-step explanation:

2(3/4)=3/2 cups per 1 person

24 x 3/2=36 cups for everyone

36 cups=18 pints

18-8=10 pints of orange juice

10 pints = 1.25 gallon

Answer:

1.25 gallons of orange juice

Step-by-step explanation:

24x2=48

3/4x48=36

36 cups into pints is 18 pints

18-8=10

10 pints into gallons is 1.25 gallons

Answer:

Small-6

Large-2

Step-by-step explanation:

small-$8

large-$16

$8×6=$48

$80-$48=$32

32÷16=2(large)

Answer:

D

Step-by-step explanation:

׳+9x²+24×+16 ...............

Answer:

A and C

Step-by-step explanation:

The triangle given has three equal sides and three equal angles.

Since the sum of a triangle = 180°, therefore, each angle equals 60°

Thus, we can conclude that the triangle is an acute triangle because an acute triangle has all three sides measuring less than 90°. This implies that all it's angles are acute angles.

Also, since all its sides are equal and the same as well as it's three angles, based on this, we can equally say the triangle is an equilateral triangle.

The triangle can be referred to as an acute triangle and also as an equilateral triangle.

Answer:

y = 500x + 1000

Step-by-step explanation:

The standadrd equation of a line is expressed as y = mx+b

m is the slope

is the y-intercept

Using the coordinate points (0, 1000) and (6, 4000)

Slope = y2-y1/x2-x1

Slope  = 4000 - 1000/6-0

Slope m = 3000/6

Slope m = 500

Since the line cut the y axis at y = 1000, hence the intercept b = 1000

Get the required equation;

Reall that y = mx+b

y = 500x + 1000

Answer:

adjacent anf o vertical

Step-by-step explanation:

Answer:

Ab^2 = CA^2 + BC^2

8^2 = 6^2 + a^2

64 = 36 + a^2

64-36 = a^2

28 = a^2

square root of 28 = square root of a^2

5 ,29 = a

5 = a

Answer:

13

Step-by-step explanation:

4w-10=42

4w=52

w=52/4

w=13

Complete question is;

A leasing firm claims that the mean number of miles driven annually, u , in its leased cars is less than 12800 miles. A random sample of 50 cars leased from this firm had a mean of 12499 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 3140 miles. Is there support for the firm's claim at the 0.05 level of significance?

Perform a one-tailed test.

null hypothesis?

alternative hypothesis?

type of test statistic?

value of the test statistic?

the p-value?

Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12800 miles?

Answer:

A) Null hypothesis; μ ≥ 12800

Alternative hypothesis; μ < 12800

B) type of test statistic: z-score test

C) test statistic; z = -0.678

D) p - value = 0.2489

E) No, we can't support the leasing firms claim

Step-by-step explanation:

We are given;

Population mean; μ = 12800 miles

Sample mean; x¯ = 12499 miles

Sample size; n = 50

Population standard deviation; σ = 3140

Let's define the hypothesis;

Null hypothesis; μ ≥ 12800

Alternative hypothesis; μ < 12800

The alternative hypothesis is the claim.

Since sample size is greater than 30, we will use z-score test.

Formula for z-score;

z = (x¯ - μ)/(σ/√n)

z = (12499 - 12800)/(3140/√50)

z = -0.678

From online p-value from z-score calculator attached, using z = -0.678 with one tailed hypothesis and significance value of 0.05,we have;

p - value = P(z < -0.678) = 0.2489

The p-value is greater than the significance value, so we will fail to reject the null hypothesis and conclude that there is no sufficient information to support the leasing firm's claim

Answer:

a)  c. 90.

b) The margin of error of the point estimate is of 6.19 minutes.

c) The minimum sample size needed to obtain this amount of precision is 289.

Step-by-step explanation:

(a) Which of the following numbers gives the value of the point estimate?

The value of the point estimate is the sample mean, of 90 minutes. So the answer is given by option c.

(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Here, we have [tex]s = 15, n = 25[/tex]. So

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.0639\frac{15}{\sqrt{25}}[/tex]

[tex]M = 6.19[/tex]

The margin of error of the point estimate is of 6.19 minutes.

Question c:

College students tend to watch sports between 0 and 120 minutes per day, which means that the standard deviation for population can be estimated as the standard deviation of an uniform distribution with [tex]a = 0, b = 120[/tex]. This standard deviation is:

[tex]\sigma = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Then

[tex]\sigma = \sqrt{\frac{(120-0)^2}{12}}[/tex]

[tex]\sigma = 34.64[/tex]

Minimum sample size:

Now, since we have an estimate for the standard deviation of the population, we use the z-distribution.

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

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

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

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The minimum sample size is n for which M = 4. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = 1.96\frac{34.64}{\sqrt{n}}[/tex]

[tex]4\sqrt{n} = 1.96*34.64[/tex]

[tex]\sqrt{n} = \frac{1.96*34.64}{4}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*34.64}{4})^2[/tex]

[tex]n = 288.1[/tex]

Rounding up:

The minimum sample size needed to obtain this amount of precision is 289.