Solve the following system of equations.
f(x) = 3x² - 7x-2
g(x) = -2x² +8

Answer:

0.341

Step-by-step explanation:

Multiply the probabilities: 0.55 * 0.62 = 0.341

The frequency table that shows the relative frequency of people older than 40 and don't visit the dentist is:

D.                  Visit Dentist Yearly Don’t Visit Dentist Yearly

Below 40                    0.27                         0.73

Above 40                   0.57                          0.43

The relative frequency of those older than 40 and don't go annually to a dentist can be found as:

= Number of over 40 who don't go to dentist / Total of those over 40 surveyed

Solving gives:

= 13 / (17 + 13)

= 13 / 30

= 0.43

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Answer:

Its D, I got it right on a test :)

Step-by-step explanation:

From the question given above, the ratio of L : W in simplified form is given as: 6 : 5. See the explanation below.

A ratio, simply, can be defined as the quantitative relationship that exists between two values which is indicative of the number of times one value can be obtained from the other.

Let X be the width of one of the rectangles and let its height be Y.

It is clear from the image that:

4X = 3Y

Hence

(4/3)X  = Y

Therefore,

Lenght (L) = 3Y

= 3 (4/3)X

= 4X

Width (W) = Y + 2X

= (4/3)X + 2X

= (10/3)X

Therefore,

L : W =  4X: 10/3X

= 4:10/3

To remove the fraction, multiply both sides of the ratio by 3

= 12 : 10, furhter simplify by halving each value, and we have

= 6:5

Hence, the ratio L: W in simplified form is 6 : 5.

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If Point T is on the line segment S U, then ST + TU = SU, Hence the length of SU is 16.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

If Point T is on the line segment S U, then ST + TU = SU

Given;

S T = 6 and T U = 10

Substitute

SU = ST + TU

SU = 6 + 10

SU = 16

Hence the length of SU is 16.

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Answer:

x-4*2

Step-by-step explanation:

Since we dont know the number, we can make it a variable. So, x is the unknown number.

4 less will mean subtraction. So. x-4.

Next we have to multiply with 2.

So, the expression is x-4*2.

Answer:

=> Apply law of cosine

[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]

=> input value

[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]

=> simplify

[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]

=> calulcation

[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]

=> apply rule: Distance must be greater than 0

which is about 14.51828

Answer:

yes

Step-by-step explanation:

yes, because there is a 99/1 chance. also, you can put 50 2010 coins in.

Answer:

the function is only increasing.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Let the unknown angle = x

   x +  43 + 90 = 180

            x + 133 = 180

                      x = 180 -133

                     [tex]\sf \boxed{\bf x = 47^\circ}[/tex]

2) x + 88 + 30 = 180

            x + 118 =180

                   x  = 180 - 118

                  [tex]\sf \boxed{\bf x = 62^\circ}[/tex]

3) x + 98 + 40 = 180

            x + 138 = 180

                    x  = 180 - 138

                    [tex]\sf \boxed{\bf x = 42^\circ}[/tex]

Answer: some perfect cubes are

8 (2^3)

27 (3^3)

64 (4^3)

there are many perfect cubes

maybe there is more to this question?

Step-by-step explanation:

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.

Answer:

see the attachment photo!

Answer:

[tex]\frac{7\sqrt{65}}{65}[/tex]

Step-by-step explanation:

Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.

[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]

The equation of the scatter plot is (a) y = 100x + 2

The line of best fit of the scatter plot passes through the points

(x,y) = (0,2) and (1,102)

Start by calculating the slope using:

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{102 - 2}{1 - 0}[/tex]

m = 100

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 100(x -0) + 2

Evaluate

y = 100x + 2

Hence, the equation of the scatter plot is (a) y = 100x + 2

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Answer:

$12

Step-by-step explanation:

x+2y=82........(1)

3x+y=96.........(2)

y=96-3x...........(3)

x+2y=82

x+2(96-3x)=82

x+192-6x=82

-5x=82-192

-5x=-110

x=-110÷-5

x=22

y=96-3x

y=96-3(22)

y=96-66

y=30

Therefore,x=22 and Y=30

so silver= x =22

gold= y = 30

y=30;x=22

=30-22

-12

Therefore $12

Answer:

[tex]\tan \dfrac{\theta}2 = \dfrac{1}2[/tex]

Step by step Explanation:

[tex]\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right][/tex]

         [tex]=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2[/tex]

Answer:

20.5 - 5.36
= 15.14/2 (because we are using perimeter, so there are 2 equal lengths and 2 equal widths)
=7.57, therefore the width of the sandbox is 7.57 ft.

Answer:

4.89 ft

Step-by-step explanation:

Perimeter of a rectangle is given by the formula :

P = 2L + 2W

So now we solve for W :

P = 2(L+W)

P/2 = L+W

P/2 - L =  W

Now we substitute our P and L into the rearranged formula :

20.5 / 2 - 5.36 = W

10.25 - 5.36 = W

W = 4.89 ft

Hope this helped and brainliest please

Answer: 2

Step-by-step explanation:

     We will first pull the data values.

0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3

     Now, we will find the middle data value. This is the median.

0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3

/,  /,  /, /, /, 2,  /,  /,  /,  /,  /

     Our median is 2.

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Using the t-distribution, it is found that the 95% confidence interval for the population mean rating for Miami is (5.73, 6.95).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.

Considering the given sample, the other parameters are given as follows:

[tex]\overline{x} = 6.34, s = 2.16, n = 50[/tex]

Hence, the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6.34 - 2.0096\frac{2.16}{\sqrt{50}} = 5.73[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6.34 + 2.0096\frac{2.16}{\sqrt{50}} = 6.95[/tex]

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Step-by-step explanation:

the answer is 94206584 kk

Answer: The save $1134.48

Step-by-step explanation:

3912 x 0.29 = 1134.48

The amount of money that the family saves in a month will be $1,017.12.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

A family has a month-to-month payment of $3912. Their month-to-month uses are displayed in the diagram underneath.

Rent 21%

Food 24%

Transportation 11%

Other Expenses 18%

Savings 26%

Then the amount of money that the family saves in a month is calculated as,

⇒ $3,912 x 0.26

⇒ $1,017.12

The amount of money that the family saves in a month will be $1,017.12.

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Answer:A. MN is a perpendicular bisector.
Hope that helps

Step-by-step explanation:

Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

Answer: 29, 31, 37, 41, 43, 47, 53.

Step-by-step explanation:

Answer:

A) x = 113°

Explanation:

Given three sides: 6.4 cm, 5.8 cm, 10.2 cm

Use the cosine rule:

c² = a² + b² - 2ab cos(C)

Insert/put variables:

[tex]\rightarrow \sf 10.2^2 = 5.8^2 + 6.4^2 - 2(5.8)(6.4) cos(x)[/tex]

[tex]\rightarrow \sf -74.24 cos(x) = 10.2^2 - 5.8^2 - 6.4^2[/tex]

[tex]\sf \rightarrow -74.24 cos(x) = 29.44[/tex]

[tex]\rightarrow \sf cos(x) = \dfrac{29.44}{-74.24}[/tex]

[tex]\rightarrow \sf x = cos^{-1}(-\dfrac{23}{58})[/tex]   = 113.36°  ≈ 113°  (rounded to nearest degree)

1) 13/40

2) 22/40

3) 5/40

☆...hope this helps...☆

_♡_mashi_♡_

Answer:

1, 4, 5, 6

Step-by-step explanation:

to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).

you can also double check by plugging both into a calculator and see if they equal the same number.

Answer:

Here,

[tex](a + b) [(a + b)(a + b)][/tex]

[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]

[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]

[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]

[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]

Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]

Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.