a 2013 study by pediatricians investigates whether it is better to give children the diphtheria, tetanus and pertussis (dtap) vaccine in the thigh or the arm. the pediatricians collected the data from two different random samples. the first random sample was collected from children who were given the vaccine in the thigh. the second random sample was collected from children who were given the vaccine in the arm. pediatricians recorded whether the children had a severe reaction or not. no severe reaction severe reaction thigh observed expected 4758 4750.9 30 37.1 arm observed expected 8840 8853.1 76 68.9 reference: jackson, l.a., peterson, d., nelson, j.c., et al. (13 co-authors). 2013. vaccination site and risk of local reactions in children one through six years of age. pediatrics 131: 283-289. pediatricians conducted a chi-square test of independence. the chi-square test statistic for this datais 2.0609 with a p-value of 0.1511. what can the pediatricians conclude? group of answer choices there is a statistically significant association between vaccine location and severe reaction. pediatricians have strong evidence that the severe reactions to vaccine depend on location of the vaccine. there is not enough evidence to conclude that there is an association between vaccine location and severe reaction. the pediatricians cannot make a conclusion. the conditions for use of the chi-square test are not met.

Answer:

no, h=anything greater than 12

Step-by-step explanation

Answer:

No. It is false.

Step-by-step explanation:

h - 2 > 10; h = 12

Substitute 12 in place of h.

12 - 2 >? 10

Simplify.

10 >? 10

10 is NOT > 10

10 is not greater than 10. 10 is equal to 10. If the symbol had the "or equal to" underline under it, then it would be true. See image.

The GCF: 2x³y

answer: 2x³y2x³y(9y³+1)

The perimeter of the resulting hexagon is 60 meters.

In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]

Where:

The perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):

p' = k · p

If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:

p' = (4 / 3) · (45)

p' = 60

The resulting hexagon has a perimeter of 60 meters.

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Answer:

3y + 4.1

Step-by-step explanation:

You can't add unlike terms, so you collect like terms:

9y - 6y + 4.1

= 3y + 4.1

The person is overwieght as his BMI is 31.00 (approx)

What is Proportion?

In general, proportion refers to a part, share, or quantity assessed in comparison to a total. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.

Solution:

Since, BMI is directly proportionate with weight and indirectly proportionate with square of height, we need to use a constant to make proportion to an equation.

According to the question,

BMI of a person who weighs 180 pounds and is 5 feet tall is 35.15.[tex]BMI = k*weight/height^{2}[/tex]

here, k is any constant value

35.15 = k*180/(60*60)

(35.15 * 3600)/180 = k

k = 703

Calculating BMI of a person weighing 210 pound and is 5 feet 9 inch tall.

First of all we need to convert 5 feet 9 inches into inches

5 feet = 60 inches

so, 5 feet 9 inch means 69 inches

BMI = 210*703/(69*69)

BMI = 31.00 (after rounding off)

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In the given coordinate plane, based on the given dilation the line r has slope 8 and coordinate (0,8)

Dilation:

Dilation refers the ratio of the given line to line by the scale factor.

Given

In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3).

Here we need to find the the slope and y-intercept of line r.

Here we know that scale factor is 3.

Let us consider the slope of the line r will not change and the intercept is the addition of their ordinate will be.

So, it can be written as,

=> Intercept = 5 + 3

=> Intercept = 8

Therefore, the line r has slope 8 and coordinate (0.8).

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Interest rate will cause his money to double in approximately 23 years is 3.13%.

Given:

Arnulfo deposited $55 into a savings account and interest is in semi annually.

For 23 years the interest payments will be = 23*2

= 46

Interest rate = 2*72 / 46

= 144/46

= 72/23

= 3.13%

Therefore Interest rate will cause his money to double in approximately 23 years is 3.13%.

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Answer:

==========================

The triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.

First, let us understand the SAS congruency theorem:

This one denotes Side - Angle - Side and it means that if 2 sides and one angle of a triangle are equal to the corresponding 2 sides and one angle of another triangle, then they are both congruent.

We are given:

SR and ST are straight lines.

side SX ≅ side SY

side XR ≅ side YT

So,

side SR ≅ side ST

In triangle RSY and triangle TSX;

side SR ≅ side ST (above proved)

∠RSY ≅ ∠TSX (Common)

side SY ≅ side SX (Given)

So, triangle RSY ≅ triangle TSX by SAS congruency theorem.

Thus, the triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.

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Answer: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Well let Krutica’s age = x

K = x,    G = x+5,    D = x-6

K+G+D = 86  

x + x+5 + x-6 = 86

3x = 87

x = 29

Gordon is the eldest of the few:

29 or x+5=

34 years old

Answer: Gordon is 34 years old

Answer:

Obtuse Angles

Step-by-step explanation:

Both < 3 and < 6 are visibly over 90° and less than 180°, so both are obtuse.

Answer:

-32

Step-by-step explanation:

-(4)^2 - -2^4 = -16 - 16 = -32

Answer:

[tex]\boxed{\boxed{\sf s=\frac{1}{3}}\sf \:or\:\boxed{\sf s=0.33...}}[/tex]

Step-by-step explanation:

[tex]\sf 3\left(s+1\right)-8=6s\left(2-4\right)[/tex]

Expand ( Apply the Distributive Property):-

[tex]\sf 3s-5=-12s[/tex]

Add 5 to both sides:-

[tex]\sf 3s-5+5=-12s+5[/tex]

Simplify:-

[tex]\sf 3s=-12s+5[/tex]

Add 12s to both sides:-

[tex]\sf 3s+12s=-12s+5+12s[/tex]

Simplify:-

[tex]\sf 15s=5[/tex]

Divide both sides by 15:-

[tex]\sf \cfrac{15s}{15}=\cfrac{5}{15}[/tex]

Simplify:-

[tex]\sf s=\cfrac{1}{3}[/tex]

___________________

Hope this helps!

Have a great day! :)

Answer:

============================

Use equation for continuous compound:

Plug in the values and calculate:

Answer:

$5,252.53 (nearest cent)

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]

[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]

[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]

[tex]\implies \sf A=5252.53457...[/tex]

Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).

Answer: 5x2x2x3x3 is the answer to your question

Answer:

[tex]3a^4b^2-2a^2b+9a[/tex]

Step-by-step explanation:

Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:

[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]

We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:

[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]

Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:

[tex]3a^4b^2-2a^2b+9a[/tex]

Answer:

A. 70.2

Step-by-step explanation:

solve your equation step-by-step.

842.412=x1

Step 1: Cross-multiply.

842.412=x1

(842.4)*(1)=x*(12)

842.4=12x

Step 2: Flip the equation.

12x=842.4

Step 3: Divide both sides by 12.

12x12=842.412

x=70.2

Hope this helps! :D

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Answer:

A. Yes, they have the same slope and a different y-intercept.

Step-by-step explanation:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Rearrange 3x + y = 6 to y = mx + c form.

y = -3x + 6

Parallel lines have the same slope.

Since slope of both lines is -3, the lines are parallel.

a. The smallest number of M & M's possible is 14.

b. The number of green is 24.

c. The ratio of green to yellow to red in 6: 15: 25.

a. When there are only green and yellow M & M's in the bag, the smallest number of M & M's possible will be:

= (2 × 2) + (2 × 5)

= 4 + 10

= 14

b. If there are 84 total green and yellow M & M's in the bag, the number of green will be:

= 2 / (2 + 5) × 84

= 2/7 × 84

= 24 green

c. If red M & M's were added to the bag in part b to get a total of 100, the ratio of green to yellow to red in simplest form will be:

= Green : Yello : Red

= 24 : 60 : 100

= 6 : 15 : 25

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Examining the given graph the number of computers infected in

The graph shows that the function is an exponential function

represented as

The starting term of the function  f(x) = 4^t is 1, and base is 4

f(x) = number of computer infected

t = time in hours

90 minutes in hours

90 / 60 = 1.5 hours

for t = 1.5 hours

f(x) = 4^1.5

f(x) = 8

for t = 6 hours

f(x) = 4^6

f(x) = 4096

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Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

Given that,

Luke asserts that since the shape is constant, two circles are always isometric.

We have to say is he accurate.

The answer is

No, an isometry keeps the size and shape intact.

Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.

Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.

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All angles of a square are 90° regardless of the length of its sides. However, all sides must be the same length.

A square is a term to refer to a geometric figure that is characterized by the following characteristics:

One key to identifying a square and the value of its angles is to add them together. The sum of the angles of any geometric figure must result in 360°.

Additionally, if we mark the diagonals of a square we must take into account that these angles will have a different value. To find this value we must divide the angle in half, because these diagonals divide the figure into two parts.

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The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.

The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:

Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:

(-20, y) = [tex](x_1, y_1)[/tex]

(-11, 15) = [tex](x_2, y_2)[/tex]

m = 0

Substitute the values into the slope formula:

0 = (15 - y) / (-11 -(-20))

0 = (15 - y) / 9

Multiply both sides by 9

0 = 15 - y

0 + y = 15 - y + y

y = 15

The answer is: a. 15.

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Answer:

1) 1 A. Yes B. Because the change in x and y is constant

2) 2 A. No B. Although the change in y is

constant, the change in x is not

3) 5. A. No B.Because the change in y is not constant

4) 4,5 A. yes B.Because the change in x and constant

Step-by-step explanation:

The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .

For the given question,

The expression is-

(s + 6) ÷ s

Use the options;

A : s = 1

= (s + 6) ÷ s

= (1 + 6) ÷ 1

= 7

B : s = 2

= (s + 6) ÷ s

= (2 + 6) ÷ 2

= 4

C : s = 3

= (s + 6) ÷ s

= (3 + 6) ÷ 3

= 3

D : s = 4

= (s + 6) ÷ 4

= (4 + 6) ÷ 4

= 2.5

Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.

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Answer:

Step-by-step explanation:

You can use proportions to solve this.

You are paying $116.64 for 3 gallons of paint, so you could write this as:

\frac{116.64}{3}

Since the question is asking for price PER CUP, you want to convert 3 gallons to cups. 3 gallons = 48 cups. So now you can rewrite this as:

\frac{116.64}{48 cups}

In order to find the cost per cup, you can set up a proportion that solves for the price, x

\frac{116.64}{48 cups}  = \frac{x}{1 cup}

Solve for x by cross multiplying:

48x = 116.64

x = $2.43

It costs $2.43 per cup of paint

The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].

What are Exponents?

What are the Laws of Exponents?

There are major seven Laws of Exponents as follows:

From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex]    -----(1)

Here, we can use the power of a power rule to simplify the expression.

The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]

Solving expression (1) using the power of a power rule, we get

[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]

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Answer:  Choice C

[tex]64m^3-32m^2+43m-15[/tex]

==================================================

Explanation:

Multiply out the expressions using the distribution rule as shown below.

[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]

I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.

Footnotes: