ow Important Is Regular Exercise? In a recent poll1 of 1000 American adults, the number saying that exercise is an important part of daily life was 753. Use StatKey or other technology to find a 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life. Click here to access StatKey. Round your answer to three decimal places. The 90% confidence interval is Enter your answer; the 90% confidence interval, value 1 to Enter your answer; the 90% confidence interval, value 2 . 1Rasmussen Reports, "75% Say Exercise is Important in Daily Life," March 26, 2011. eTextbook and Media

Answer:

Part a) [tex]m<HIG=40\°[/tex]

Part b) IHG is a semicircle and GJI is a semicircle

Part c) HIJ is a major arc and HIJG is a major arc

Part d) [tex]arc\ GH=80\°[/tex]

Part e) [tex]arc\ GJI=180\°[/tex]

Step-by-step explanation:

Part a) Give an inscribed angle

we know that

The inscribed angle measures half that of the arc comprising

so

in this problem m<HIG is an inscribed angle

[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]

[tex]arc\ HG=80\°[/tex] ----> by central angle

substitute

[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]

Part b) Give a semicircle

we know that

The diameter divide the circle into two semicircles

so

GI is a diameter

therefore

IHG is a semicircle

GJI is a semicircle

Part c) Give a major arc

we know that

The measure of a major arc is greater than 180 degrees

therefore

HIJ is a major arc

HIJG is a major arc

Part d) Measure of arc GH

we know that

[tex]arc\ GH=m<HFG[/tex] ----> by central angle

so

[tex]arc\ GH=80\°[/tex]

Part e) Measure of arc GJI

we know that

[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle

the answer is 942.because the formula is V=Bh. V=pir2h. so V= 3.14×5squared×12. so 3.14×25×12. 25×12=300. and 3.14×300=942

Answer:

6x-5y=-10

Step-by-step explanation:

We are given an equation in words and we are to translate it and then re-write its standard form:

'y space equals space 6 over 5 x space plus space 2 '

[tex] y = \frac { 6 } { 5 } x + 2 [/tex]

Re-arranging this given equation to get:

[tex] y - 2 = \frac { 6 } { 5 } x [/tex]

[tex]5(y-2)=6x[/tex]

[tex]5y-10=6x[/tex]

[tex]6x-5y=-10[/tex]

So the correct answer option is 6x-5y=-10.

Answer:

a. Ratio of girls to all students 5:11

b. Ratio of girls to all students n:m+n

c. Ratio of girls to boys 5:6

Step-by-step explanation:

In order to find each of these, we simply need to look at these as a comparison of two data points.

a. In this example, we are looking for girls to all students. We already who there would be 5 girls in the comparison. Then we need to find the whole amount, which is girls + boys (6 + 5 = 11)

5:11

b. In this example, we are looking for girls to all students. We already who there would be n girls in the comparison. Then we need to find the whole amount, which is girls + boys (m + n)

n:m+n

c. In this example, we are looking for girls to boys. We already who there would be 5 girls in the comparison. Then we need to find the boys amount, which is whole - girls (11 - 5 = 6)

5:6

Final answer:

The ratio of girls to all students in a class with a boy-girl ratio of 6 to 5 is 5 to 11. The general ratio of girls to all students with a boy-girl ratio expressed as m:n is n:(m+n). Lastly, if five elevenths of the class are girls, then the ratio of girls to boys is 5 to 6.

Explanation:

Understanding Ratios in a Classroom Setting

The ratio of boys to girls in a class is initially given as 6 to 5. To find the ratio of girls to all the students in the class, the sum of the parts of the ratio must first be calculated, which is 6 (boys) + 5 (girls) = 11 (total students).

Therefore, the ratio of girls to the total number of students is 5 to 11. This is because for every 11 students, 5 are girls. If the ratio of boys to girls is expressed as m:n, then the ratio of girls to all students will be n:(m + n).

For a scenario where five elevenths of the class are girls, the ratio of girls to boys needs to be determined. As five elevenths represent the girls, six elevenths must represent the boys, since they sum up to the whole, which is one (or 11/11). Therefore, the ratio of girls to boys is 5:6.

Answer: [tex]x=-1[/tex]

Step-by-step explanation:

By the negative exponent rule, you have that:

[tex](\frac{1}{a})^n=a^{-n}[/tex]

By the exponents properties, you know that:

[tex](m^n)^l=m^{(nl)}[/tex]

Therefore, you can rewrite the left side of the equation has following:

[tex](\frac{1}{8})^{-(2x+7)}=(\frac{1}{32})^{3x}[/tex]

 Descompose 32 and 8 into its prime factors:

[tex]32=2*2*2*2*2=2^5\\8=2*2*2=2^3[/tex]

Rewrite:

[tex](\frac{1}{2^3})^{-(2x+7)}=(\frac{1}{2^5})^{3x}[/tex]

Then:

[tex](\frac{1}{2})^{-3(2x+7)}=(\frac{1}{2})^{5(3x)}[/tex]

As the base are equal, then:

[tex]-3(2x+7)=5(3x)[/tex]

Solve for x:

[tex]-6x-21=15x\\-21=15x+6x\\-21=21x\\x=-1[/tex]

D using the foil method

Answer: [tex]4x^2+17x-15[/tex]

Step-by-step explanation:

To simplify the given expression we need to apply the distributive property in algebra.

The distributive property is given by :

[tex]a(b+c)=ab+ac[/tex]

The given expression:

[tex](4x- 3)(x + 5)\\\\=(4x-3)x+(4x-3)5\ \ \ \ \text{By distributive property}\\\\=4x^2-3x+20x-15\\\\=4x^2+(-3+20)x-15\ \ \ \text{Combining like terms}\\\\=4x^2+17x-15[/tex]

The other root of the quadratic equation is -2, and the coefficient c is -106, found using the sum and product of roots formulas.

The other root and the coefficient c of the quadratic equation 10x²- 33x + c = 0, given that one of the roots is 5.3. Using the fact that the sum of the roots of a quadratic equation ax² + bx + c = 0 is equal to -b/a, we can find the other root. With one root known to be 5.3 and a = 10, b = -33, the sum of the roots must be 3.3. Therefore, the other root is 3.3 - 5.3 = -2. To find the coefficient c, we use the fact that the product of the roots of a quadratic equation is equal to c/a. Thus, c = 5.3 * (-2) * 10 = -106. The other root of the equation is -2, and the coefficient c is -106.

Answer:

  C)  78 ft

Step-by-step explanation:

The side opposite the angle has the ratio to the hypotenuse:

  Sin = Opposite/Hypotenuse

Then the solution to this problem is found by substituting the given information and solving for the height.

  sin(45°) = height/(110 ft)

  (110 ft)·sin(45°) = height ≈ 77.7817 ft

Rounded to the nearest foot, the crane can raise material to a height of 78 ft.

Answer:

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

Answer:

  Triangles BPA and DPC are congruent.

Step-by-step explanation:

The statement above is the only one of the bunch that is true, so is the best selection.

You don't even need to worry too much about how you might make the proof. You just need to be concerned with which are plausible answers. There's only one.

Answer:

  4 units

Step-by-step explanation:

The sides of the rectangle are parallel to the axes, so it is a simple matter to subtract coordinate values to find the dimensions.

Along the line y=7, the rectangle extends from -5 to 5, so has width 10.

Along the line x=5, the rectangle extends from 1 to 7, so has length 6.

The width is 10 - 6 = 4 units more than the length.

Answer: width=7 length =9

9-7=2

2 is the answer

ANSWER

[tex]y = - 5[/tex]

EXPLANATION

The horizontal asymptote of a general exponential function,

[tex]f(x) = a {(b)}^{x} + c[/tex]

is y=c.

The given exponential function is

[tex]f(x) = 4{(2)}^{x} - 5[/tex]

By comparing the given function to

[tex]f(x) = a {(b)}^{x} + c[/tex]

we have c=-5, therefore the horizontal asymptote is

[tex]y = - 5[/tex]

Answer:

y= -2x/3+8

Step-by-step explanation:

find 2 points: (0,8) and (6,4)

substitute in y=ax+b

8=0a+b

b=8

4=6a+b

4=6a+8

6a=-4

a=-2/3

simplify :7x + 3x - 5 + 8x + 5 = 180

x = 10

Answer:

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}[/tex]

We have:

[tex]DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788[/tex]

Substitute:

[tex]\dfrac{75}{0.9659}=\dfrac{EF}{0.788}[/tex]          cross multiply

[tex]0.9659EF=(75)(0.788)[/tex]

[tex]0.9659EF=59.1[/tex]          divide both sides by 0.9659

[tex]EF\approx61.19[/tex]

The length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have:

DE = 75 inches

By using the sin law:

sin52/EF = sin75/DE

sin52/EF = sin75/75

sin52/EF = 0.0128

EF = 61.185 ≈ 61.19 inches

Thus, the length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

Here is your answer

[tex]<b>z= 20 degrees</b>[/tex]

REASON:

[tex]<font color="blue" size=5>Concept used</font>[/tex]: The sum of adjacent angles of a parallelogram is 180 degrees.

So, in above given figure

[tex] 2z+16+124=180 [/tex] (measures of adjacent angles)

[tex]2z+140=180 [/tex]

[tex] 2z=180-140 [/tex]

[tex]2z=40 [/tex]

[tex]z= 40/2 [/tex]

[tex]z= 20 [/tex]

HOPE IT IS USEFUL

Answer:

300%

Step-by-step explanation:

600 / 120 = 300

Answer:

  a straight line: y = x -5, with a hole at (4, -1)

Step-by-step explanation:

The rational function can be simplified to ...

  [tex]f(x)=\dfrac{x^2-9x+20}{x-4}=\dfrac{(x-5)(x-4)}{(x-4)}\\\\f(x)=x-5\qquad\text{$x\ne 4$}[/tex]

The graph of this is a straight line, with a hole at x=4, where the function is not defined.

Answer:

$13.68

Step-by-step explanation:

3.42 x 4

Final answer:

To find the total cost of 4 baseballs, each costing $3.42, we multiply the cost of one baseball by the number of baseballs, resulting in a total cost of $13.68.

Explanation:

The question asks to calculate the total cost of 4 baseballs, provided that each costs $3.42. To find the total cost, we need to multiply the cost of one baseball by the number of baseballs that were purchased. Hence, the calculation of the total cost of baseball is given by $3.42 (cost of one baseball) × 4 (number of baseballs) = $13.68. Therefore, the total cost of the 4 baseballs is $13.68.

Answer:

  90°

Step-by-step explanation:

Supplementary means they add to 180°. Vertical angles are congruent, so they must both be 180°/2 = 90°.

Answer:

90

Step-by-step explanation:

Did the Geometry quiz 2021

Plz click the Thanks button!

<Jayla>

Answer:

B. x = 4

Step-by-step explanation:

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

[tex]\log_bm+\log_bn=\log_bmn[/tex]

Using this law, we can combine and rewrite our initial equation as

[tex]\log_2(x\cdot(x-2))=3\\\log_2(x^2-2x)=3[/tex]

Remember that logarithms are simply another way of writing exponents. The logarithm [tex]\log_28=3[/tex] is just another way of writing the fact [tex]2^3=8[/tex]. Keeping that in mind, we can express our logarithm in terms of exponents as

[tex]\log_2(x^2-2x)=3\rightarrow2^3=x^2-2x[/tex]

2³ = 8, so we can replace the left side of our equation with 8 to get

[tex]8 = x^2-2x[/tex]

Moving the 8 to the other side:

[tex]0=x^2-2x-8[/tex]

We can now factor the expression on the right to find solutions for x:

[tex]0=(x-4)(x+2)\\x=4, -2[/tex]

The only option which agrees with our solution is B.

Answer:

The answer is:

        [tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]

Step-by-step explanation:

We are given a logarithmic expression as:

[tex]\log_2 x+log_2 (x-2)=3[/tex]

As we know that:

[tex]\log_a x=\dfrac{\log x}{\log a}[/tex]

Hence, we get the logarithmic expression as follows:

[tex]\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}=3[/tex]

We know that we can get the system of equations as follows:

[tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}[/tex]

and

[tex]y_2=3[/tex]

Hence, when we plot the graph for this system of equations we see that the point of intersection of the graph is: (4,3)

Hence, the solution is the x-value of the point of intersection of the two equations.

Hence, x=4 is the solution.

Hence, the correct option is:

  [tex]y_1=\dfrac{\log x}{\log 2}+\dfrac{\log (x-2)}{\log 2}\ ,\ y_2=3\ ,\ x=4[/tex]

if it is asking for compound interest your answer should be 49761.9

Answer:

No solution.

Step-by-step explanation:

The given functions are

[tex]y=\cos2x[/tex] and [tex]y=1-\sin^2x[/tex].

To find the point of intersections of the graphs of the two functions: we equate them and solve for [tex]x[/tex].

[tex]\cos2x=1-\sin^2x[/tex]

Recall the double angle identity; [tex]\cos2x=cos^2x-sin^2x[/tex]

Apply this identity to obtain;

[tex]cos^2x-sin^2x=1-\sin^2x[/tex]

[tex]\Rightarrow cos^2x=1[/tex]

[tex]\cos x=\pm1[/tex]

[tex]x=0\:or\:x=\pi[/tex]

if the interval is [tex]0\le x\le \pi[/tex], then the two graphs intersect at [tex]x=0\:or\:x=\pi[/tex]

But [tex]x=0\:and\:x=\pi[/tex] does not belong to the open interval [tex]0\:<\:x\:<\:\pi[/tex]

No point of intersection.

Answer:

YES

YES

NO

YES

Step-by-step explanation:

Assuming that the value is [tex]\dfrac{4}{9}[/tex].

Let's take each of the equations and check if the fraction makes the equation true.

When multiplying a whole number to a fraction, it is the same as multiplying the whole number to the numerator and dividing the total by the denominator.

[tex]63*\dfrac{4}{9}=28[/tex]

[tex]\dfrac{63*4}{9}=28[/tex]

[tex]\dfrac{252}{9}=28[/tex]

[tex]28=28[/tex]    YES

[tex]18*\dfrac{4}{9}=8[/tex]

[tex]\dfrac{18*4}{9}=8[/tex]

[tex]\dfrac{72}{9}=8[/tex]

[tex]8=8[/tex]    YES

[tex]96*\dfrac{4}{9}=42[/tex]

[tex]\dfrac{96*4}{9}=42[/tex]

[tex]\dfrac{384}{9}=42[/tex]

[tex]42.67=42[/tex]    NO

[tex]36*\dfrac{4}{9}=16[/tex]

[tex]\dfrac{36*4}{9}=16[/tex]

[tex]\dfrac{144}{9}=16[/tex]

[tex]16=16[/tex]    YES

Answer:

yes

yes

no

yes

hope this helps!!

Answer:

(3250/100)*80 = $ 2600 - 3250 = $650

Step-by-step explanation:

1/2÷1/6

=

1/2*6/1

=

6/2

=

3

Answer:

Quotient would be 3.

Step-by-step explanation:

The model below can be used to find the quotient of one over two dividend by one over six.

We will rewrite the problem :

[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{6}[/tex]

As we know when we divide the two fractions, we must invert the second fraction and put the sign of multiplication in place of division sign and multiply.

So now we can write the problem as :

[tex]\frac{1}{2}[/tex] × [tex]\frac{6}{1}[/tex]

= [tex]\frac{6}{2}[/tex]

= 3

Quotient would be 3.

Answer:D) 144

Step-by-step explanation:12*12=144

Answer:

the answer is 144

Step-by-step explanation:

Answer:

[tex]\large\boxed{-6y^2+12y+4}[/tex]

Step-by-step explanation:

[tex](2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4[/tex]

Answer:

$455.97

Step-by-step explanation:

119000 × 0.12 = 14280

119000 - 14280 = 104720

104720 × 1.045 = 109432.4

109432.4/(20×12)

109432.4/240

455.97 a month

Answer:

$662.46

Step-by-step explanation: