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Answer:

4 cm, 7 cm, 11 cm

Step-by-step explanation:

The sum of two shorter sides of a triangle is always greater than the larger side.

1 cm + 5 cm < 7 cm ( can't be the third side )

5 cm + 4 cm > 7 cm ( can be )

5 cm + 7 cm > 7 cm ( can be )

5 cm + 7 cm > 11 cm ( can be )

5 cm + 7 cm < 13 cm ( can't be )

5 cm + 7 cm < 15 cm ( can't be )

Answer:

$117.25

Step-by-step explanation:

To solve, multiply the interest by the total amount in savings.

You can calculate simple interest in a savings account by multiplying the account balance by the interest rate by the time period the money is in the account. Here's the simple interest formula: Interest = P x R x N. P = Principal amount (the beginning balance).

Brenda get $117.25 as interest from her bank.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Brenda learned that her bank would pay her 5% on her money in her savings account if she had at least $1,000 in it.

Brenda had $2,345 in her savings account.

So, the interest Brenda get

= 2345 x 5/ 100

= 2345 x 0.05

= $117.25

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Answer:

Assuming that this data is used to conduct a hypothesis test to test the manufacturers' claim, the test statistic we an use is:

the paired sample t-test.

Step-by-step explanation:

a) Data and Analysis:

Subject   Before   After

1                 225      215

2                245     240

3                 188      188

4                210       212

5               282       175

6               275      260

7               230      225

8               195      200

9               190       185

b) The paired sample t-test is used to compare the means from the same dataset but at different times (say, one month apart).  It supports the comparison of sample data before and after the data subjects have taken the dietary supplement.  When the t-value is high, it is an evidence that the null hypothesis should be rejected.  The higher value of the t-test, therefore, indicates that there is a large difference between the two sample sets.  On the other hand, a small t-value shows similarity between the two sample sets.

Answer:

CI 99% = (  0,022  ;  0,126 )

Step-by-step explanation:

First sample  

n₁  = 500

x₁  = 48

p₁ = x₁ / n₁   =  48 / 500      p₁  =  0,096      p₁  = 9,6 %

Second sample

n₂  = 400

x₂  = 68

p₂ = x₂ / n₂   =  68 / 400      p₂  =  0,17       p₂  = 17 %

CI = 99 %    significance level α = 1 %     α  = 0,01

z(c)  for α = 0,01  is from z- table    z(c) = 2,325

CI  =  ( p₂ - p₁ ) ±  z(c) *√ p*q* ( 1/n₁  +  1 / n₂ )

Where

p₂  -  p₁  =  0,17 - 0,096 = 0,074

p = ( x₁ + x₂ )  / n₁ + n₂

p =  ( 48  +  68  ) /( 500 + 400)

p = 116/ 900     p = 0,1288     and   q = 1 - p     q  = 0,8712

z(c) *√ p*q* ( 1/n₁  +  1 / n₂ ) = 2,325 * √ 0,1288*0,8712 ( 1 / 500 + 1/ 400)

2,235 * 0,02247

z(c) *√ p*q* ( 1/n₁  +  1 / n₂ ) = 0,052

Then

CI 99 %  =  0,074  ±  0,052

CI 99% = (  0,022  ;  0,126 )

The difference between the groups shows that the proportion in the second group was bigger than in the first group.

The CI in the context of the problem is  CI 99% = (  0,022  ;  0,126 )

Given first sample is  

n₁  = 500

x₁  = 48

  [tex]P_{1} =\dfrac{X_{1} }{n_{1} }[/tex]      [tex]P_{1} =\dfrac{48}{500}[/tex]      

p₁  =  0,096      p₁  = 9,6 %

Given second sample

n₂  = 400

x₂  = 68

[tex]P_{2} =\dfrac{X_{2} }{n_{2} }[/tex]      [tex]P_{2} =\dfrac{68}{400}[/tex]        

p₂  =  0,17       p₂  = 17 %

Since given CI = 99 %    so significance level  α = 1 %     α  = 0,01

From Z-Table  z(c)  for α= 0,01  is = 2,325

CI  =   [tex](P_{2} -P_{1}[/tex]   ±    [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]  

Where

p₂  -  p₁  =  0,17 - 0,096 = 0,074

[tex]P= \dfrac{X_{1} +X_{2} }{n_{1}+n_{2} }[/tex]

[tex]P=\dfrac{48+68}{500+400}[/tex]

[tex]P=\dfrac{116}{900}[/tex]

p = 0,1288     and   q = 1 - p     q  = 0,8712

[tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )[/tex]  [tex]2325\times\sqrt[2]{0.1288\times 0.8712} (\dfrac{1}{500_{} } +\dfrac{1}{400_{} } )[/tex]

  [tex]Z(c)\sqrt[2]{p\times q} (\dfrac{1}{n_{1} } +\dfrac{1}{n_{2} } )=0.052[/tex]

Then

CI 99 %  =  0,074  ±  0,052

CI 99% = (  0,022  ;  0,126 )

Hence the difference between the groups shows that the proportion in the second group was bigger than in the first group.

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Answer: it's 10, not 210.

Answer:

$28.35

Step-by-step explanation:

[tex]45\% \times 63 \\ = 0.45 \times 63 \\ = 28.35[/tex]

Answer:

square side = 57

hexagon side = 38

Step-by-step explanation:

x = side length of square

y = side length of hexagon

x = y + 19

4x = 6y

substitute for x:

4(y + 19) = 6y

4y + 76 = 6y

subtract 4y from each side of the equation:

2y = 76

divide both sides by 2:

y = 38

x = 57

Answer:

Hi there,

Make the side of the hexagon = x

Side of square = x + 12

Both figures have the same perimeters.

4(x + 14) = 6x

4x + 56 = 6x

Collect like terms:

6x - 4x = 56

2x = 56

x = 28

Length of hexagon side = 28 feet

Length of square side = 42 feet

Hope this helps :-)

The expression of 5.39 × 10⁷ metric tons in standard notation is; 53,900,000 metric tonnes

We are given the quantity of wheat produced each year as 5.39 × 10⁷ metric tons.

Now, that quantity is in exponent form and the way to express it in standard notation is to expand the exponent which gives;

5.39 × 10⁷ = 5.39 * 10 * 10 * 10 * 10 * 10 * 10 * 10

⇒ 5.39 * 10000000

⇒ 53,900,000 metric tonnes

The complete question is;

The U.S. produces 5.39 × 10⁷ metric tons of wheat each year. Express that number in standard notation

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Answer:

area of triangle = 1/2 b×h

Step-by-step explanation:

108=1/2×b×12

108×2=12b

216/12=b

18=b

Answer:

83

Step-by-step explanation: st had this question

Answer: 80

Step-by-step explanation:

Just substitute 1 for x in your expression and solve

Answer:

The correct answer is "9√2 units".

Step-by-step explanation:

The given equations are:

⇒ [tex]3x^2-y^2=3[/tex]...(equation 1)

⇒ [tex]y+x-5=0[/tex]...(equation 2)

According to the 2nd equation, we get

⇒ [tex]y+x-5=0[/tex]

⇒              [tex]y=5-x[/tex]

On substituting the value of "y" in the 1st equation, we get

⇒  [tex]3x^2-y^2=3[/tex]

     [tex]3x^2-(5-x)^2=3[/tex]

     [tex]3x^2-(25+x^2-10x)=3[/tex]

     [tex]2x^2+10x-28=0[/tex]

On taking common, we get

     [tex]x^2+5x-14=0[/tex]

On applying factorization, we get

     [tex]x^2+7x-2x-14=0[/tex]

   [tex]x(x+7)-2(x+7)=0[/tex]

           [tex](x+7)(x-2)=0[/tex]

                        [tex]x+7=0[/tex]

                              [tex]x=-7[/tex]

or,

                         [tex]x-2=0[/tex]

                                [tex]x=2[/tex]

Now,

The points are:

(-7, 12) = (x₁, y₁)

(2, 3) = (x₂, y₂)

By using the distance formula, the length of chord will be:

= [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

On substituting the values in the above formula, we get

= [tex]\sqrt{(2-(-7))^2+(3-12)^2}[/tex]

= [tex]\sqrt{(9)^2+(-9)^2}[/tex]

= [tex]\sqrt{81+81}[/tex]

= [tex]9 \sqrt{2}[/tex] units

A regular polygon has equal side lengths and congruent interior angles.

The sum of the interior angles of any regular polygon is determined using the formula: (n - 2)180, where n is the number of sides.

Thus, given polygon GHIJK has 5 sides, we would have the following:

The polygon is a regular pentagon.

Sum of all its interior angles = (5 - 2)180 = 540°.

Each interior angle = 540/5 = 108°

Therefore, the statement that is true about the regular polygon are:

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Answer: b, c, e

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

a square has 4 sides.

100/4=25

Answer:

e. obtaining data with a small p-value.

Step-by-step explanation:

In the null hypothesis, we test if the mean respects certain condition, and on the alternate hypothesis, we test the opposite of the null hypothesis.

The decision depends on the pvalue:

If the pvalue is smaller than the level of significance, that is, the pvalue has small values, the null hypothesis is rejected, that is, it is strong evidence against the null hypothesis. Large pvalues do not give evidence against the null hypothesis.

So the correct answer is given by option e.

Answer:

63degrees

Step-by-step explanation:

Using the theorem which states that the measure of angle at the vertex is half the angle of its intercepted arc.

Given

angle of its intercepted arc = 126 degree

Required

angle at the vertex = x =<XYZ

According to the theorem;

x = 1/2(126)

x = 126/2

x = 63

Hence the measure of <XYZ is 63degrees

Answer:

y = sin(x + 90°)

Step-by-step explanation:

cos 0 = 1

Since the point (0, 1) is on the graph, this graph is y = cos x, but that is not a choice, so this must be the graph of the sine function with a horizontal translation.

sin 0 = 0

sin 90° = 1

The translation is 90°.

Answer: y = sin(x + 90°)

Answer:

Step-by-step explanation:

x(x+8) = 450

x² + 8x - 450 = 0

Quadratic formula:

x = [-8±√(8²-4(1)(-450))]/[2(1)]

= [-8±2√466]/2

= -4±√466

≅ 17.59, -25.59

-25.59 is an extraneous solution, so x ≅ 17.6 inches.

The dimensions of the blackboard are 17.59 inches by 25.59 inches  

Answer:

exponent

Step-by-step explanation:

Answer:

power or exponent it can be both, but being specific here, choose exponent

Step-by-step explanation:

i studied this concept trust me

Answer:

it is option C

Step-by-step explanation:

download  to help your work

1/ a cube and b to the power 4

9514 1404 393

Answer:

  A.  translation 8 left

Step-by-step explanation:

Points X'Y'Z' are in the same clockwise order as points XYZ, so no reflection is involved.

Point X' at -6 is 8 units left of point X at 2. ΔXYZ has been translated left 8 units to make ΔX'Y'Z'.

Answer:

a is the answer.

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

angle A +angle B +angle C = 180

30° +B+90°= 180

120°+B=180°

B=180°-120°

B=60°

Answer:

I think angle 7 could also measure 117, and I think the angle relationship is alternate exterior angles.

Step-by-step explanation:

If my answers are wrong, I am incredibly sorry!

H⁣⁣⁣⁣ere's l⁣⁣⁣ink t⁣⁣⁣o t⁣⁣⁣he a⁣⁣⁣nswer:

bit.[tex]^{}[/tex]ly/3a8Nt8n

Answer:

Solutions for x are 2, 1/3

Everything in the second image is correct except you forgot to put 2 for c in the quadratic formula.

Answer:

:)

Step-by-step explanation:

Answer:

que

Step-by-step explanation:

no sé

Answer:

20 / (3 + c)

Step-by-step explanation: