is 1 1/3 a unit rate

Answer:

4 balloons for each balloon animal.

Step-by-step explanation:

Amira sells balloon animals. The given table compares the number of balloon animals sold and the remaining number of balloons on a certain day.

Animals        Balloons

15                   200

24                   164

33                   128

When she sold 15 animals the leftover balloons were 200.

then she sold 24 animals the number of leftover balloons were 164.

The difference of the number of items = 24 - 15 = 9 more animals sold

The difference of the leftover balloons = 200 - 164 = 36 balloons used

Now the number of her sold animals was = 33

and the left over balloons = 128

The number of sale was increased by 24 to 33 = 33 - 24 = 9 more animals

and the leftover balloons now 164 to 128 = 164 - 128 = 36 used

Therefore, we can see each sale of 9 balloon animals she used 36 balloons.

so Amira used for each balloon animal = [tex]\frac{36}{9}[/tex]

                                                                = 4 balloons.

Amira used 4 balloons for each balloon animal.

Answer:

The most she can sell is 65

Step-by-step explanation:

"How many balloon animals at most can Amira sell?"

Answer:

g(x)=(x+4)^2+5(x+4)-6

The actual answer to this equation is x=19 not x=1 or n=0

The correct answer is 6. In other words, the value of m that satisfies the solving linear equation is m = 6.

In the given equation, we are asked to find the value of m. The equation states that the quantity 5m minus 1 is equal to the quantity 4m plus 5.

To solve this equation, we can use algebraic methods. The goal is to isolate the variable m on one side of the equation.

First, we combine like terms. By subtracting 4m from both sides of the equation, we eliminate the term with m on the right side. This results in the equation m - 1 = 5.

Next, we isolate the variable m by adding 1 to both sides of the equation. This cancels out the -1 term on the left side and gives us m = 6.

Therefore, the correct answer is 6. In other words, the value of m that satisfies the solving linear equation is m = 6.

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[tex]n+n+1+n+2+n+3=4n+6[/tex]

4n is divisible by 4, but 6 is not, so the sum 4n+6 is not divisble by 4.

Answer:c.

No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%

Step-by-step explanation:

Summation of the cost of loan =200+530+600+265+575+130+800

=3100

Now percentage of the estimate=

(3100/50000)*100%

=6.2%

C- The lender should not consider them as reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3-5%.

The lender cannot be accepting these costs as this will lead to the lender incurring losses over a longer period after doing all the necessary calculations.

[tex]200+530+600+265+575+130+800=3100[/tex]

[tex]\frac{3100}{50000} *100= 6.2[/tex]

Hence, the correct option is C that the amounts of $3100 are not a reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between the range of 3-5%.

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The graph of the line change is, It will shift down 6 units.

The given function is,

y = 15x + 2

Now, We want to find how the graph of this function will change if the function is transformed to

y = 15x  -4

We rewrite this function in terms of the first one to get:

y = 15x + 2 + (-6)

Hence, the function with shift down 6 units.

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Answer: The exact circumference of the circle is [tex]10\pi[\tex] in.

Step-by-step explanation:

Since, the circumference of a circle is,

[tex]C=2\pi r[/tex]

Where, r is the radius of the circle,

Here, r = 5 inches,

Hence, the circumference of the circle is,

[tex]C = 2\pi(5) = 10\pi\text{ in}[/tex]

Thus, The exact circumference of the circle is [tex]10\pi[\tex] in.

Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.

Which statement is true about lines a and b?

Answer:

Bank charges fee to non customers while using ATM. ATM's frequently charge fees to users who are not account holders from that same bank whose ATM you are operating.

This fee goes towards the compensation for the costs associated with owning and operating the machine.

Same bank persons pay many types of fee yearly to their banks, so same bank ATM do not charge any fee.

When using other banks, your bank has to pay some interchange amount to that bank, this is also the reason why banks charge fee, basically they recoup the money that they will have to pay to other banks for interchange.

The use of the normal distribution as an approximation for the sampling distribution of[tex]\( \bar{p} \)[/tex] requires both [tex]\( np \)[/tex] and [tex]\( n(1 - p) \)[/tex] to be at least 5. So, the answer is (b) 5.

The normal approximation for the sampling distribution of [tex]\( \bar{p} \),[/tex] the sample proportion, relies on the conditions that both[tex]\( np \)[/tex] and [tex]\( n(1 - p) \)[/tex] are greater than or equal to 5. Here, [tex]\( n \)[/tex]  represents the sample size, and [tex]\( p \)[/tex] is the probability of success in a binary outcome. These conditions ensure that the distribution of[tex]\( \bar{p} \)[/tex] is approximately normal, allowing for the application of statistical techniques based on the normal distribution. When[tex]\( np \)[/tex]and [tex]\( n(1 - p) \)[/tex]are both at least 5, the central limit theorem asserts that the distribution of [tex]\( \bar{p} \)[/tex] is sufficiently close to normal, facilitating the use of standard normal tables and z-scores for making probability calculations and inferences about the population proportion. This approximation is pivotal in hypothesis testing and confidence interval construction for proportions in statistical analyses.

Answer:

Option A.

Step-by-step explanation:

The table made by the painter shows the amount of paint required to cover a certain amount of area of the wall.

Amount of paint is directly proportional to the area covered

In other words Amount of paint (y) ∝ Area covered (x)

y ∝ x

As we know when proportionality sign is removed, a constant known as proportionality constant is multiplied with the variable.

So y = k(x) where k is the proportionality constant

Now from the table to cover the area of 64 square feet, 4 pints of paint is required.

Now from the formula

4 = 64x

x = [tex]\frac{4}{64}=\frac{1}{16}[/tex]

Now we have to calculate the amount of paint required to cover the area of 256 square feet.

y = [tex]\frac{1}{16}\times 256[/tex]

y = 16 pints

Therefore, 16 pints of the paint will be required to cover 256 square feet.

Option A is correct.

Answer:

Just Pick 16 Pints

Step-by-step explanation:

Answer:

The dimensions are [tex]35\times 14\times 5[/tex] and the volume is 2450 inches³.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 45 in. by 24 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '45-2x'.

The breadth of the box is '24-2x'.

The volume of the box is [tex]V=L\times B\times H[/tex]

[tex]V=(45-2x)\times (24-2x)\times x[/tex]

[tex]V(x)=4x^3-138x^2+108x[/tex]

Derivate w.r.t x,

[tex]V'(x)=4(3x^2)-138(2x)+108[/tex]

[tex]V'(x)=12x^2-276x+108[/tex]

[tex]V'(x)=12(x^2-23x+90)[/tex]

The critical point when V'(x)=0

[tex]12(x^2-23x+90)=0[/tex]

[tex]x^2-23x+90=0[/tex]

[tex](x-18)(x-5)=0[/tex]

[tex]x=18,5[/tex]

18 is not possible we reject.

So, the height is 5 inches.

Derivate again w.r.t x,

[tex]V''(x)=24x-276[/tex]

[tex]V''(5)=24(5)-276[/tex]

[tex]V''(5)=120-276[/tex]

[tex]V''(5)=-156<0[/tex]

i.e. V(x) is maximum at x=5.

The dimensions are

Height = 5 inches

Length = 45-2(5)=35 inches

Breadth = 24-2(5)=14 inches.

The maximum volume is

[tex]V=35\times 14\times 5[/tex]

[tex]V=2450[/tex]

So, The dimensions are [tex]35\times 14\times 5[/tex] and the volume is 2450 inches³.

The points on the circle x² + y² = 100 where the slope of the tangent is ¾ are (6, -8) and (-6, 8). This is found by taking the derivative of the circle equation, setting it equal to the slope, solving for y, substituting this into the original circle equation, and solving for x.

The equation of the circle is x² + y² = 100. To find the points on this circle where the slope of the tangent is ¾, we need to find the derivative of this equation. The derivative of y with respect to x is dy/dx = -x/y. Set this equal to ¾ and solve for y, which gives y = -4x/3. Substitute this into the original circle equation to solve for x, which yields x = ± 6. Then substitute these x-values back into the equation y = -4x/3 to get y = ± 8. Therefore, the points on the circle where the slope of the tangent is ¾ are (6, -8) and (-6, 8).

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Final answer:

To find points on the circle x² + y² = 100 where the slope is 3/4, differentiate the circle's equation and set the derivative equal to 3/4. Solve the system of equations involving the circle's equation and the line's equation derived from the slope criteria. This process typically yields two points of intersection due to the geometrical properties of circles and lines.

Explanation:

To find all points on the circle x2 + y2 = 100 where the slope is 3/4, we first acknowledge that the given circle is centered at the origin (0,0) with a radius of 10 units. Since the slope of a tangent to the circle at any point can be found using implicit differentiation, let's differentiate the given equation with respect to x. Doing so, we get 2x + 2yy' = 0 where y' denotes the slope of the tangent to the circle at (x,y). Solving for y', we get y' = -x/y. Setting this equal to the given slope of 3/4, we have -x/y = 3/4.

By cross-multiplying and rearranging, we get 4x + 3y = 0. To find the points of intersection between the line and the circle, we substitute x2 + y2 = 100 into this equation. Solving the system of equations will yield the points on the circle where the slope of the tangent is 3/4.

Note: The exact points of intersection would require solving a resulting quadratic equation, which can give two possible points since a line with a given slope (except vertical) will typically intersect a circle at two points.