There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.

What is the theoretical probability of randomly drawing a red marble?

20%
41.7%
62.5%
25%

Option C: [tex]f(x)=2^x[/tex] is the function rule.

Explanation:

The sequence is [tex]2,4,8,16, \dots \dots[/tex]

Let us find the common difference of this sequence.

Common ratio = [tex]\frac{4}{2} =2[/tex]

Hence, [tex]r=2[/tex]

Thus, the given sequence is a geometric progression.

To determine the function rule, let us substitute the values in the general formula of GP which is given by

[tex]f(x)=ar^{x-1}[/tex] where [tex]a=2, r=2[/tex]

Substituting we get,

[tex]f(x)=2(2)^{x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2\times2^x\times2^{-1[/tex]

Adding the powers, we get,

[tex]f(x)=2^{1+x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2^x[/tex]

Hence, the function rule is [tex]f(x)=2^x[/tex]

Thus, Option C is the correct answer.

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Solution:

Given roots of the polynomial are:

–3, –2, 1 and 5

If a is the root of the polynomial then the factor is (x –a).

So that, the factors of the given roots are:

(x –(–3)) = x + 3

(x –(–2)) = x + 2

(x – 1) = x – 1

(x – 5) = x –5

Polynomial = Product of the factors

                    = (x + 3)(x + 2)(x – 1)(x – 5)

Multiply first two factors.

                     [tex]=(x^2+2x+3x+6)(x-1)(x-5)[/tex]

                     [tex]=(x^2+5x+6)(x-1)(x-5)[/tex]

Now, multiply the next two factors.

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

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

Now multiply these two factors.

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

                     [tex]=x^4-6x^3+5x^2+5x^3-30x^2+25x+6x^2-36x+30[/tex]

                     [tex]=x^4-x^3-19x^2-11x+30[/tex]

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Answer:

2 5/8 to 1.

Step-by-step explanation:

That would be 1  3/4 divided by 2/3.

= 7/4 / 2/3

= 7/4 * 3/2

= 21 / 8

= 2 5/8

Answer 2 5/8 to 1.

I think

Answer:

  the net amount is due in 45 days

Step-by-step explanation:

Invoice terms often have a discount for early payment, and a specification as to the date by which payment in full is expected. n/45 means the net amount of the invoice is due in 45 days.

Answer:

y = - 2x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2, thus

y = - 2x + c ← is the partial equation

To find c substitute (3, 2) into the partial equation

2 = - 6 + c ⇒ c = 2 + 6 = 8

y = - 2x + 8 ← equation of perpendicular line

Answer:

The difference is 40,

Step-by-step explanation:

Complementary angles , x+y =90

so we know angle 1, we call it  3x and angle 2 we call it y= 3x+10

so 3x +10= 90-x

4x=100

x=25

angle 1= 3(25) - 10

y= 65

65-25= 40

Answer:

  40°

Step-by-step explanation:

Let x represent one of the angles, and y represent the other one. Then we have ...

  x + y = 90

  3x = y +10

Substituting for y in the first equation, we have ...

  x + (3x -10) = 90

  4x = 100

  x = 25

  y = 3(25) -10 = 65

The difference between the angles is ...

  y -x = 65 -25 = 40 . . . . degrees

The difference between the angle measures is 40 degrees.

Answer:

5 - 1 = 4

Step-by-step explanation:

Option A. When m increases , n tends to increase.

Step-by-step explanation:

Positive correlation is a relationship between two variables in which both variables move in the same direction.

Option A. When m increases , n tends to increase.

Answer:

A. When m increase, n tends to increase

Answer:

[tex]\$ 36000\ down\ payment\ is=30\%\\\\\$ 42000\ down\ payment\ is=35\%[/tex]

Step-by-step explanation:

[tex]Purchase\ price=\$ 120000\\\\[/tex]

[tex]when\ down\ payment=\$ 36000\\\\percentage\ down\ payment=\frac{down\ payment}{total\ amount}\times 100\\\\percentage\ down\ payment=\frac{36000}{120000}\times 100\\\\percentage\ down\ payment=0.3\times 100=30\%[/tex]

[tex]when\ down\ payment=\$ 42000\\\\percentage\ down\ payment=\frac{down\ payment}{total\ amount}\times 100\\\\percentage\ down\ payment=\frac{42000}{120000}\times 100\\\\percentage\ down\ payment=0.35\times 100=35\%[/tex]

Final answer:

A $36,000 down payment is 30% of the $120,000 purchase price. A $42,000 down payment would be 35% of the purchase price.

Explanation:

To calculate what percent the down payment is of the purchase price, we use the formula:

(Down Payment / Purchase Price) x 100 = Percentage of Purchase Price

For the initial $36,000 down payment:

Divide $36,000 by the purchase price of $120,000 to get 0.3.

Multiply 0.3 by 100 to get 30%.

Therefore, a $36,000 down payment is 30% of the $120,000 purchase price.

For a $42,000 down payment:

Divide $42,000 by the purchase price of $120,000 to get 0.35.

Multiply 0.35 by 100 to get 35%.

A $42,000 down payment would be 35% of the purchase price.

Answer: 47 degrees

Step-by-step explanation: If it dropped form 35 to 0. That is 35 degrees, if it dropped from 0 to -12 degrees that is 12 more degrees. 35 + 12 = 47

Answer:

it dropped 47°

add 12 to 35

Answer:

Step-by-step explanation:

3.705 rounded to the nearest tenth of an oz = 3.7 <==

The weight of the sweet potato chips, when rounded to the nearest tenth, is 3.7 ounces.

To round the weight of the sweet potato chips to the nearest tenth of an ounce, we look at the number in the hundredths place.

Since the weight is 3.705, and the number in the hundredths place is 0.005, we apply a basic rounding rule: if the number in the hundredths place is 5 or more, we round up the number in the tenths place.

Here, that means we round up '7' to '8'. Thus, when rounded to the nearest tenth of an ounce, the weight of the sweet potato chips is 3.7 ounces.

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Answer:

The number is 30.

Step-by-step explanation:

x/5+3=9

x/5=9-3

x/5=6

x=6*5

x=30

The number is 30.

The given question is a mathematical equation.

Let's define the number as 'x'. According to the given equation, the quotient of the number and 5, which is x/5, when three is added to it, should be equal to 9. Mathematically, we can write this as:

x/5 + 3 = 9

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting 3 from both sides of the equation:

x/5 = 9 - 3

x/5 = 6

To get rid of the fraction, we can multiply both sides of the equation by 5:

x = 6 * 5

x = 30

Therefore, the number is 30.

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Answer:

Divide 11 by 10 . Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (1) by the divisor 10 . Subtract 10 from 11 . :) Hope this helps!

It can be a fraction of 11/10 as a mixed number is 1 1/10.

To convert a fraction into a mixed number, you need to divide the numerator (top number) by the denominator (bottom number).

The whole number part of the result is the whole number of the mixed number, and the remainder becomes the numerator of the fractional part.

As per the question, we have the fraction 11/10.

Dividing 11 by 10 gives:

11 ÷ 10 = 1 remainder 1

So the whole number part is 1, and the fractional part is 1/10. We can express this as a mixed number by writing:

11/10 = 1 1/10

Therefore, 11/10 as a mixed number is 1 1/10.

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Answer:

Viewing window: [0, 1.4] × [-3, 12]

See the attachments from the TI-83 Plus graphing calculator.

1) f(t) = -16t² + 15t + 6.5

2) -16t² + 15t + 6.5 = 0

32t² - 30t - 13 = 0

t = (30 + √((-30)² - 4(32)(-13)))/(2(32))

= (30 + √2564)/64

= (30 + 2√641)/64

= (15 + √641)/32

= about 1.26 seconds

3) f'(t) = -32t + 15

-32t + 15 = 0

t = 15/32 seconds = about .47 seconds

f(15/32) = -16(15/32)² + 15(15/32) + 6.5

= about 10.02 feet

Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]

Part 2: It takes approximately 0.89 seconds for the basketball to hit the ground.

Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.

Part 1: The function that models the height of the basketball is given by:

[tex]\[ h(t) = -16t^2 + v_0 t + h_0 \][/tex]

Given:

- Initial velocity [tex](\( v_0 \))[/tex] = 15 ft/sec

- Initial height [tex](\( h_0 \))[/tex] = 6.5 feet

So, the function becomes:

[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]

Part 2: To find how long it takes for the basketball to hit the ground, we set [tex]\( h(t) = 0 \)[/tex] and solve for [tex]\( t \)[/tex]:

[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]

We can use the quadratic formula to solve for[tex]\( t \)[/tex]:

[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where [tex]\( a = -16 \), \( b = 15 \), and \( c = 6.5 \).[/tex]

Plugging in the values:

[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \]\[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \]\[ t = \frac{-15 \pm \sqrt{641}}{-32} \][/tex]

Using a calculator, we find:

[tex]\[ t \approx 0.89 \text{ seconds (rounded to the nearest hundredth)} \][/tex]

Part 3: To find when the basketball reaches its maximum height, we can use the formula for the x-coordinate of the vertex of a quadratic function:

[tex]\[ t_{\text{max}} = -\frac{b}{2a} \][/tex]

For our function [tex]\( h(t) = -16t^2 + 15t + 6.5 \), \( a = -16 \) and \( b = 15 \).[/tex]

[tex]\[ t_{\text{max}} = -\frac{15}{2(-16)} \]\[ t_{\text{max}} = \frac{15}{32} \]\[ t_{\text{max}} \approx 0.47 \text{ seconds (rounded to the nearest hundredth)} \][/tex]

Part 4: To find the maximum height of the basketball, we substitute the value of [tex]\( t_{\text{max}} \)[/tex] into the function [tex]\( h(t) \):[/tex]

[tex]\[ h_{\text{max}} = -16(0.47)^2 + 15(0.47) + 6.5 \]\[ h_{\text{max}} = -16(0.2209) + 7.05 + 6.5 \]\[ h_{\text{max}} = -3.5344 + 7.05 + 6.5 \]\[ h_{\text{max}} \approx 10.0156 \text{ feet (rounded to the nearest hundredth)} \][/tex]

The maximum height of the basketball is approximately 10.02 feet.

Answer:

A: 900 yards

Step-by-step explanation:

im sure... i had the same test question and got it right! pls give me brainliest

Answer:

900 sq. yd.

Step-by-step explanation:

So, we know that the baseball diamond is a square, so we use the equation of a square, A = [tex]a^{2}[/tex]

Since all sides of a square are equal, each is always gonna be 30 yards. So we substitute a for 30

A = [tex]a^{2}[/tex]

A = [tex]30^{2}[/tex]

A = 900 sq. yd.

Which gives you the area of the diamond as 900 sq. yd.

Answer:

(2m)^3(m^4)^5= 8m^23

(-3y^5)^3x2y^2= -54y^17

Step-by-step explanation:

1.  For solving first part

  (2m)^3(m^4)^5

   =[tex](2^3 m^3) (m^{20} )\\Acoording \,to\,exponential\,rules \, exponent 4 \, and\, 5 \,were\, \,multiplied\\As\\\2^3 =8 \\so\\8m^3 \times m^{20} \\\\Acoording \,to\,exponential\,rules \, exponent \,3 \,and\,20\,will\,be\,added\\x^{2} 8m^{23}[/tex]

(2m)^3(m^4)^5= 8m^23

2. For solving second part

(-3y^5)^3 x 2y^2

[tex](-3^3) y^{5\times3} \times 2y^2\\\\As \,3^3= 27 \,and\\\\applying \,exponential\, rule \,the\, exponents\ 5 \, and\, 3 \,will\,be\,multiplied\\the \,equation will become\\-27 \,y15 \times 2y^2\\\\applying \,exponential\, rule \,the\, exponents\, 15 \,and\, 2 \,wil, be\,added \\-54 y^{17}[/tex]

(-3y^5)^3 x 2y^2= -54y^17

Keywords: Algebra

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The inequality p > 64 represents the total number of pieces he has ⇒ D

Step-by-step explanation:

Let us revise the inequality words

∵ Ashton makes more than 32 sandwiches for a party

∴ The number of sandwiches > 32

∵ Ashton cuts each sandwich into two pieces

- That the number of pieces is the number of sandwiches times 2

∴ The number of pieces > 2 × 32

∴ The number of pieces >  64

- The number of pieces is p

∴ p > 64

The inequality p > 64 represents the total number of pieces he has

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Answer:

The system of inequalities is given by

i) x + y ≥ 10

ii) 9x + 4y ≤ 100

Step-by-step explanation:

i) let x be the number of grams of fat in the non-carb brownie.

ii) let y be the number of grams of protein in the non-carb brownie.

iii) The brownie must weigh at least 10 grams

iv) therefore we can write x + y ≥ 10

v) The brownie must have no more than 100 calories

vi) therefore we can write 9x + 4y ≤ 100

Answer:

I = 0.015x

Step-by-step explanation:

To calculate the interest obtained from your investment after one year, multiply the interest rate by the investment.

You can use the formula I = Prt; where:

"I" is interest (Capital i).

"P" is principal, starting money or investment.

"r" is the interest rate converted to decimal form.

"t" is the time, usually in years.

Convert 1 1/2% to decimal form. First, change the mixed fraction percentage to a decimal percentage. Convert the percentage to decimal form by dividing by 100. This value will be "r". (Don't confuse decimal form with decimal form as a percentage).

1 1/2% = 1.5%

1.5% ÷ 100 = 0.015

r = 0.015

From the problem, we know the time is 1 year; t = 1.

We don't know the value for the principal, "P", but we are told to use the variable "x"; P = x

Using the bolded information, substitute them for the variables into the formula.

I = Prt

I = (x)(0.015)(1)     Remember any number multiplied by "1" is not changed.

I = (x)(0.015)       Change the standard formatting without brackets.

I = 0.015x         Formula for the interest obtained after 1 year.

Interest obtained after 1 year in dollar is 0.015x

Given that;

Number of year = 1

Number of dollars invested = x

Rate of interest = [tex]1\frac{1}{2}[/tex]%

Find:

Interest obtained after 1 year

Computation:

Rate of interest = [tex]1\frac{1}{2}[/tex]%  = 3/2 % = 1.5% = 0.015

Interest = (P)(R)(T)

Interest obtained after 1 year = (x)(1)(0.015)

Interest obtained after 1 year = 0.015x

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Answer:

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates.

Answer:no

Step-by-step explanation:

It'll be may 15th

if She starts on May 5 then there is no practice on May 19.

Two or more expressions with an Equal sign is called as Equation.

Given that Vicky has baseball practice every 10 days

She starts on May 5 .

We have to find whether she has to practice on May 19.

From May 5 the ten days ends at may 15.

So on May 19 the practice is not there.

So no, Vicky does not practice on May 19.

Hence, if She starts on May 5 then there is no practice on May 19.

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Answer:

The missing side is 7

Step-by-step explanation:

The smaller triangle has the same exact angles and the bigger one. If you notice each side with a value is three times the smaller one. 8m times three equals 24m. So if we divide 21 by 3 we get 7

Answer: 7

Step-by-step explanation:

Answer:

Right

Step-by-step explanation:

Triangle having ninety degree angle in it is right angle triangle.

Solving the inequality [tex]2+s\geq 10\,\,,where\,\,s=7[/tex] we get [tex]9\geq 10\,\,(not\,\,true)[/tex]

We know that 9 is not greater than 10 so, the inequality doesn't hold.

Step-by-step explanation:

We need to solve:

[tex]2+s\geq 10\,\,,where\,\,s=7[/tex]

Solving the inequlaity:

[tex]2+s\geq 10[/tex]

Putting value of s i.e s=7 in the equation

[tex]2+7\geq 10\\9\geq 10[/tex]

Solving the inequality [tex]2+s\geq 10\,\,,where\,\,s=7[/tex] we get [tex]9\geq 10\,\,(not\,\,true)[/tex]

We know that 9 is not greater than 10 so, the inequality doesn't hold.

Keywords: Solving inequalities

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Answer:

75%

Step-by-step explanation:

you have to divide 135 by 180 which you look like, 135/180. then once you receive a decimal/fraction which would be .75 you can turn that into a percentage which would be 75%. hope this helped

Answer:

2) D

12) C

13) D

Step-by-step explanation:

2)     4° C at 6:00 PM

A)  + 2°  - 6° = - 4°          4°  -  4°  = 0°       0° does not equal 4°        A  [tex]\neq[/tex] Correct

B)   - 5°  + 1° = - 4°           4°  -  4°  = 0°       0°  does not equal 4°      B  [tex]\neq[/tex] Correct

C)  + 6° - 4° =  + 2°          4° + 2° = 6°           0° does not equal 4°      C  [tex]\neq[/tex] Correct  

D)  - 7°   + 7° = 0°            4°  + 0°  = 4°          4°  does equal 4°           D = Correct

The answer to question #2 is D

12)  M = -3

N ---->  M = 8.5 units

The only possible options for N are:

-3 + 8.5 = 5.5

-3 - 8.5 = -11.5

-11.5 is not a choice, so the answer to question #12 is C

13)  Scale: 1 inch = 70 yards

Abe walks 3.5 inches (on the diagram)

Multiply both sides of the scale by 3.5

3.5 * 1 inch = 70 * 3.5

3.5 inches = 245 yards

Abe walked 245 yards

The answer to question #13 is D

Hope this helps :)

Rate of commission as a percent is 12 %

Solution:

Kara weekly paycheck is $6,500 including her salary which is $1,000

Therefore,

Commission amount = Weekly paycheck - salary

Commission amount = 6500 - 1000

Commission amount = 5500

Her sales for the week totaled to $45,000

Therefore rate of commission is given as:

[tex]Commission\ rate = \frac{\text{commission amount}}{\text{sales for week}} \times 100[/tex]

Substituting the values we get,

[tex]Commission\ rate = \frac{5500}{45000} \times 100\\\\Commission\ rate = \frac{550}{45}\\\\Commission\ rate = 12.2 \approx 12[/tex]

Thus rate of commission as a percent is 12 %

Answer:

V=-27

Step-by-step explanation:

8v+1=7v-26

-7v -7v

v+1=-26

-1 -1

v=-27