And Investment Of $2700 Is Made For Eight Months I Have An Annual Simple Interest Rate Of 2.25% What (2024)

Given

h(t)=30.5t+8.7

Find

Meaning of slope

Meaning of y-intercept

Explanation

(a)

Slope = 30.5

It means the average speed of the hot air balloon is 30.5 ft/min

(b)

y-intercept = 8.7

It means the initial height of the balloon is 8.7 ft

Final Answer

(a) 30.5

(b) 8.7

To solve fo x, equate all the angles to 180 degree

That is;

x + x - 5 + x - 28 = 180 (sum of angle in a triangle)

3x -33 = 180

Add 33 to both-side

3x =213

Divide both-side by 3

x = 71

The angles are;

x = 71°

x - 5 = 71 - 5 =66°

x - 28 = 71 - 28 =43°

The Solution:

Given:

We are asked to find the volume.

Observe that the base surface that can give a uniform cross-section is a trapezoid.

So, the formula for the volume is:

[tex]Volume=\frac{1}{2}(a+b)h\times H[/tex]

In this case:

[tex]\begin{gathered} a=1m \\ \\ b=4m \\ \\ h=height\text{ of the trapezoid}=? \\ \\ H=10m \end{gathered}[/tex]

Find h:

[tex]\begin{gathered} h^2+3^2=30^2 \\ \\ h^2=900-9 \\ \\ h^2=891 \\ \\ h=\sqrt{891}=29.8496m \end{gathered}[/tex]

Substitute:

[tex]Volume=\frac{1}{2}(1+4)29.85\times10=5\times29.85\times5=746.241m^3[/tex]

Therefore, the correct answer is 746.241 cubic meters.

Explanation

We are given the following:

• 13 balls numbered 1 through 13 placed in a bucket.

We are required to determine the probability of randomly drawing two balls numbered 12 and 2 without replacement, in that order.

This is achieved thus:

The probability of randomly selecting a ball numbered 12 from the bucket is:

[tex]Pr.(12)=\frac{1}{13}[/tex]

The probability of randomly selecting 2 from the bucket after the first selection is:

[tex]Pr.(2)=\frac{1}{12}[/tex]

Therefore, the probability of randomly selecting two balls numbered 12 and 2 is:

[tex]\begin{gathered} Pr.=\frac{1}{13}\times\frac{1}{12} \\ Pr.=\frac{1}{156} \end{gathered}[/tex]

Hence, the answer is:

[tex]\frac{1}{156}[/tex]

We have to prove that:

[tex]\angle VWX\cong\angle YZX[/tex]

And we are given that:

[tex]\begin{gathered} \bar{WV}\parallel\bar{YZ} \\ X\text{ is the midpoint of }\bar{VY} \end{gathered}[/tex]

Statement 1:

[tex]\bar{WV}\parallel\bar{YZ}[/tex]

Reason: Given

Statement 2:

[tex]\text{There are lines that passes through WV and YZ}[/tex]

Reason: Postulate of existence of lines

Statement 3:

[tex]\text{The line WZ is tranversal to WV and YZ}[/tex]

Reason: Information given on the graph.

Statement 4:

[tex]\angle VWX\cong\angle YZX[/tex]

Reason: Alternate interior angles are congruent.

Determine the additional cost of housing for a month.

[tex]2590-1975=615[/tex]

Determine the additional cost of housing for a year.

[tex]12\cdot615=7380[/tex]

The moving charge is 545

We will see how to determine independent probabilities of two events with the help of set notations.

We will define two events that can occur independently as follows:

[tex]\begin{gathered} \text{Event ( E ) = Corn crop infected by earth worms} \\ \text{Event ( B ) = Corn crop infected by corn borers} \end{gathered}[/tex]

The probability of occurrence of each event is defined by the prefix " p " preceeding each event notation as follows:

[tex]\begin{gathered} p\text{ ( E ) = 0.18} \\ p\text{ ( B ) = 0.11} \\ \text{p ( E \& B ) = 0.06} \end{gathered}[/tex]

We can express the two events ( E and B ) as two sets. We will Venn diagram to express the events as follows:

We have expressed the two events E and B as circles which are intersecting. The region of intersection is the common between both events ( E & B ).

The required probability is defined as an instance when the corn crop is subjected to either earth worm or corn borers or both!

If we consider Venn diagram above we can see the required region constitutes of region defined by event ( E ) and event ( B ). We can sum up the regions defined by each event!

However, if we consider region E and B as stand alone we see that the common region is added twice in the algebraic sum of induvidual region E and B. We will discount the intersection region once to prevent over-counting. Therefore,

[tex]p\text{ ( E U B ) = p ( E ) + p ( B ) - p ( E \& B )}[/tex]

The above rule is the also denoted as the rule of independent events ( probabilities ).

We will use the above rule to determine the required probability p ( E U B ) as follows:

[tex]\begin{gathered} p\text{ ( E U B ) = 0.18 + 0.11 - 0.06} \\ p\text{ ( E U B ) = 0.23} \end{gathered}[/tex]

Therefore, the required probability is:

[tex]0.23\ldots\text{ Option D}[/tex]

Answer:

x = - 9

Explanation:

The given equation is

- 5x + 7 = 52

We want to solve for x

Subtracting 7 from both sides, it becomes

- 5x + 7 - 7 = 52 - 7

- 5x = 45

Dividing both sides of the equation by - 5, we have

- 5x/- 5 = 45/- 5

x = - 9

Answer:

(-∞, -4] U [1, ∞)

Explanation:

The given function is:

[tex]f(x)=2(x-1)(x+4)^3[/tex]

Since f(x) ≥ 0, we are going to find the range of values of x for which f(x) ≥ 0

By carefully observing the graph shown:

f(x) ≥ 0 for values of x less than or equal to -4, and also for values of x greater than or equal to 1.

This can be written mathematically as:

x ≤ -4 or x ≥ 1

This can be written in interval notation as:

(-∞, -4] U [1, ∞)

From the question

Percentage markup = 26%

Selling price(SP) = $350

To find the Markup

The formula below will be used

[tex]\text{ \%Markup }=\frac{SP-CP}{CP}-100\text{\%}[/tex]

Since Cost price(CP) is not given

Hence, substitute given values to find CP

[tex]26=\frac{350-CP}{CP}\times100[/tex]

Solve for CP

Cross multiply

[tex]26CP=100(350-CP)[/tex]

Expand the bracket

[tex]26CP=35000-100CP[/tex]

Collect like terms

[tex]\begin{gathered} 26CP+100CP=35000 \\ 126CP=35000 \end{gathered}[/tex]

Divide both sides by 126

[tex]\begin{gathered} \frac{126CP}{126}=\frac{35000}{126} \\ CP=\text{ \$}277.78 \end{gathered}[/tex]

Hence the cost price is $277.78

To find Markup the formula below will be used

[tex]\text{Markup }=SP-CP[/tex]

Hence,

[tex]\begin{gathered} \text{Markup }=\text{ \$}350-\text{ \$}277.78 \\ \text{Markup }=\text{ \$}72.22 \end{gathered}[/tex]

Therefore, the markup is $72.22

The geometric sequence is given by:

[tex]a_n=a\cdot r^{n-1}[/tex]

where:

a = first term of the sequence

r = common ratio

so:

[tex]\begin{gathered} n=7 \\ a_7=6\cdot2^{7-1} \\ a_7=6\cdot2^6 \\ a_7=6\cdot64 \\ a_7=384 \end{gathered}[/tex]

ANSWER

Ten-millionths

EXPLANATION

We want to find the place value of 9 in 8.00231497.

The number 9 is placed 7 places beyond the decimal point. This implies that its value is 7 orders of 10 less than 8 and its place value is ten-millionths.

That is the answer.

Given:

Radius of the circle = 50 cm

Central angle = 1/10 rad

Let's find the area of the sector.

To find the area of the sector, apply the formula:

[tex]Area=\frac{1}{2}\times r^2\theta[/tex]

Where:

r is the radius = 50 cm

θ is the central angle in radians = 1/10 radian

Hence, we have:

[tex]\begin{gathered} \text{Area}=\frac{1}{2}\times50^2\times\frac{1}{10} \\ \\ \text{Area}=\frac{1}{2}\times2500\times\frac{1}{10} \\ \end{gathered}[/tex]

Solving further:

[tex]Area=\frac{1\times2500\times1}{2\times10}=\frac{2500}{20}=125\operatorname{cm}^2[/tex]

Therefore, the area of the sector of the circle is 125 square centimeters.

ANSWER:

125 cm²

Solution

The length of a rectangle is five times its width.

Let the length be represented by L

Let the width be represented by W

The length of the rectangle is five times the width i.e

[tex]L=5W[/tex]

To find the perimeter, P, of a rectangle, the formula is

[tex]P=2(L+W)[/tex]

Given that the perimeter, P, of the rectangle is 120ft,

Subsitute for length and width into the formula above

[tex]\begin{gathered} P=2(L+W) \\ 120=2(5W+W) \\ 120=2(6W) \\ 120=12W \\ \text{Divide both sides by 12} \\ \frac{12W}{12}=\frac{120}{12} \\ W=10ft \end{gathered}[/tex]

Recall that, the length of the rectangle is

[tex]\begin{gathered} L=5W \\ L=5(10) \\ L=50ft \\ W=10ft \end{gathered}[/tex]

To find the area, A, of a rectangle, the formula is

[tex]A=LW[/tex]

Substitute the values of the length amd width into the formula above

[tex]\begin{gathered} A=(50)(10)=500ft^2 \\ A=500ft^2 \end{gathered}[/tex]

Hence, the area of the rectangle is 500ft²

Notice that the given triagle is a right triangle. Remember the definition of the cosine of an angle on a right triangle.

[tex]\cos (\theta)=\frac{\text{Side adjacent to }\theta}{\text{ Hypotenuse}}[/tex]

Plugging in the information of the diagram:

[tex]\cos (\angle SQR)=\frac{SQ}{QR}[/tex]

Substitute the given values of each segment:

[tex]\cos (29)=\frac{5}{x}[/tex]

Isolate x and use a calculator to find a decimal expression for x:

[tex]\begin{gathered} x=\frac{5}{\cos (29)} \\ \Rightarrow x=5.716770339\ldots \\ \Rightarrow x\approx5.7 \end{gathered}[/tex]

Therefore, the length of the side QR, to the nearest tenth of a foot is:

[tex]5.7[/tex]

11)

Given data:

The given pair of traingles.

The expression for the ratio of the coorresponding sides is,

[tex]\begin{gathered} \frac{5}{x}=\frac{2}{1} \\ 5=2x \\ x=2.5 \end{gathered}[/tex]

Thus, the value of x is 2.5.

13)

Given data:

The given pair of rectangles.

The expression for the ratio of the corresponding sides is,

[tex]\begin{gathered} \frac{3}{x}=\frac{4}{6} \\ 18=4x \\ x=\frac{18}{4} \\ =4.5 \end{gathered}[/tex]

Thus, the value of x is 4.5.

Hello!

First, let's graph all these functions in the graph below:

• green,: first function

,

• blue,: second function

,

• red,: third function

As we can see, the first and the second grow almost the same (lines are very near), while the third grows faster.

A proportional relationship can be said to be a relationship between two variables with equivalent ratios. Here the two variables vary directly with each other.

Thus, using the equation:

y = kx

where k is the constant

Here, we have:

d = 65t

where 65 is the constant of proportionality

We can say d varies directly as t

Therefore d = 65t is proportional.

ANSWER:

Proportional

We have to find two points from the graph to find the slope of the line equation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-2}{0-(-4)}=-\frac{2}{4}=-\frac{1}{2}[/tex]

We took the points (-4, 2) and (0, 0)

x1 = -4

y1 = 2

x2 = 0

y2 = 0

Then, using the point-slope form of the line equation, we have, for point (0, 0):

[tex]y-0=-\frac{1}{2}(x-0)\Rightarrow y=-\frac{1}{2}x[/tex]

Then, the constant of variation is k = -1/2 and y = (-1/2)x.

The given expression is

(1/2)(x - y) -4

When applying the ditributive property, we multiply each term inside the bracket by the term outside the bracket. Thus, we have

1/2 * x - 1/2 * y - 4

= x/2 - y/2 - 4

Thus, the correct option is C

Answer:

The quotient is; (the whole number)

[tex]6[/tex]

and the remainder is;(numerator of the fraction)

[tex]5[/tex]

Each day they will hike:

[tex]6\frac{5}{12}[/tex]

Explanation:

From the question, it was given that they have to hike a total of 77 miles in 12 days.

total distance = 77 miles

Total time = 12 days

To get the distance they will hike per day, we will divide the total distance by the total time.

[tex]\begin{gathered} r=\frac{77}{12}=\frac{72+5}{12} \\ r=\frac{72}{12}+\frac{5}{12} \\ r=6+\frac{5}{12} \\ r=6\frac{5}{12} \end{gathered}[/tex]

Therefore, The quotient is; (the whole number)

[tex]6[/tex]

and the remainder is;(numerator of the fraction)

[tex]5[/tex]

In a group of samples find the deviation

there are 160 students

mean is the sum of samples/ number of samples

standard deviation is a number defined by

Deviation = √ sum of squares = 1

Then find number of students with readings more than 85g

looking at the curve. 80 students are measuring more than 85g, and substracting deviation standard= 1 . The result more precise is 80-1= 79 students

38 faces

Explanation:

Amount to be earned = $100

Amount spent on supplies = $16

This is an expenses on the business

Amount charged per face = $3

Let x represent the number of faces to be painted

The total calculation:

[tex]\begin{gathered} 100=\text{ 3x -16} \\ 100+16\text{ = 3x} \\ 116\text{ = 3x} \\ \text{Divide through by 3} \\ x\text{ =}\frac{116}{3} \\ x\text{ = 38.67} \\ Since\text{ number of faces can't be decimal or fraction,} \\ we\text{ will approxi}mate\text{ to 39 faces} \end{gathered}[/tex]

Note: $16 was subtracted because it was an expense and to make a profit of $100, it snould not include expenses.

Therefore, the number of faces she needs to paint to meet her $100 goal is 38 faces.

The addition of the 3 probabilities must be equal to 1.

1) P(A) + P(B) + P(C) = 5/10 + 2/10 + 1/10 = 4/5 ≠ 1

2) P(A) + P(B) + P(C) = 0 + 1/2 + 1/2 = 1

3) P(A) + P(B) + P(C) = 1/5+ 1/6 + 1/3 = 7/10 ≠ 1

4) a probability can't be negative

Then, the correct option is option 2

Answer:

[tex]\begin{gathered} CP=\sqrt{11} \\ m\operatorname{\angle}C=56.44 \end{gathered}[/tex]

Explanation:

Step 1. The information that we have is that

• PQ=5

,

• CQ=6,

and that PQ is tangent to circle C.

Since PQ is a tangent line, it forms a 90° angle with the circumference, and the triangle is a right triangle.

We need to find CP and the measure of angle C (m

Step 2. To find CP we use the Pythagorean theorem:

In this case:

[tex](CQ)^2=(CP)^2+(PQ)^2[/tex]

Substituting the known values:

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

Solving for CP:

[tex]\begin{gathered} 6^2-5^2=(CP)^2 \\ 36-25=(CP)^2 \\ 11=(CP)^2 \\ \sqrt{11}=CP \end{gathered}[/tex]

The value of CP is:

[tex]\boxed{CP=\sqrt{11}}[/tex]

Step 3. To find the measure of angle C, we use the trigonometric function sine:

[tex]sinC=\frac{opposite\text{ side}}{hypotenuse}[/tex]

The opposite side to angle C is 5 and the hypotenuse is 6:

[tex]sinC=\frac{5}{6}[/tex]

Solving for C:

[tex]C=sin^{-1}(\frac{5}{6})[/tex]

Solving the operations:

[tex]\begin{gathered} C=s\imaginaryI n^{-1}(0.83333) \\ C=56.44 \\ \downarrow \\ \boxed{m\operatorname{\angle}C=56.44} \end{gathered}[/tex]

Answer:

[tex]\begin{gathered} CP=\sqrt{11} \\ m\operatorname{\angle}C=56.44 \end{gathered}[/tex]

In order to find the inverse of this conditional, we need to negate both the first and second statement.

So we have:

First statement: "Tracy is not going to Quinn's candy shop"

Second statement: "she is not going to buy sour straws"

Negating these, we have:

First statement: "Tracy is going to Quinn's candy shop"

Second statement: "she is going to buy sour straws"

So the inverse will be:

"If Tracy is going to Quinn's candy shop then she is going to buy sour straws.​"

[tex]\begin{gathered} \text{The sample space for a coin is 2} \\ S=(H,T) \\ \text{Thus, probability of tossing a head is:} \\ Pr(H)=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{The sample space for a die is 6} \\ S=(1,2,3,4,5,6) \\ \text{Thus, the probability of rolling a number greater than 4 is:} \\ Pr(>4)=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]

Hence, the probability of tossing a head and then rolling a number greater that 4 is:

[tex]\begin{gathered} \frac{1}{2}\times\frac{1}{3} \\ \Rightarrow\frac{1}{6} \\ \Rightarrow0.167 \end{gathered}[/tex]

Given:

[tex]y=-2x-3[/tex][tex]y=2x^2+4x-1[/tex]

Requires:

We need to solve the given system of equations.

Explanation:

Consider equation.

[tex]y=2x^2+4x-1[/tex][tex]Substitute\text{ }y=-2x-3\text{ in the equation to find the value of x.}[/tex][tex]-2x-3=2x^2+4x-1[/tex]

Add 2x+3 to both sides of the equation.

[tex]-2x-3+2x+3=2x^2+4x-1+2x+3[/tex][tex]0=2x^2+6x+2[/tex][tex]2x^2+6x+2=0[/tex]

Divide both sides of the equation by 2.

[tex]\frac{2x^2}{2}+\frac{6x}{2}+\frac{2}{2}=\frac{0}{2}[/tex][tex]x^2+3x+1=0[/tex]

Which is of the form

[tex]ax^2+bx+c=0[/tex]

where a=1, b=3, and c =1.

Consider the quadratic formula.

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

Substitute a=1, b=3, and c =1 in the equaiton.

[tex]x=\frac{-3\pm\sqrt{3^2-4(1)(1)}}{2(1)}[/tex][tex]x=\frac{-3\pm\sqrt{9-4}}{2}[/tex][tex]x=\frac{-3\pm\sqrt{5}}{2}[/tex][tex]x=\frac{-3\pm\sqrt{5}}{2}[/tex]

We need to create a table as follows:

Yellow pieces Green pieces Yellow/Green

5 50 - 5 = 45 5/45 = 0.11

10 50 - 10 = 40 10/40 = 0.225

15 50 - 15 = 35 15/35 = 0.4286

25 50 - 25 = 25 25/25 = 1

35 50 - 35 = 15 35/15 = 2.333

45 50 - 45 = 5 45/5 = 9

We define the number of yellow pieces, then we calculate the number of green pieces taking into account that the sum of yellow and green is 50.

Finally, we found the relation between yellow and green pieces. The answer is going to be the row where the division between the yellow and green pieces is 9. Because that division tells us how many Yellow pieces are for every green piece.

Answer: 45 yellow pieces

[tex]\begin{gathered} T(x)=\frac{13}{5}+\frac{32}{5(3x+1)^2} \\ T(1)=\text{ }\frac{13}{5}+\text{ }\frac{32}{5(3(1)+1)^2} \\ T(1)=\frac{13}{5}+\frac{32}{5(4)^2} \\ T(1)=\frac{13}{5}+\frac{32}{5(16)} \\ T(1)=\frac{13}{5}+\frac{2}{5} \\ T(1)=\frac{15}{5}=3 \\ \end{gathered}[/tex][tex]\begin{gathered} T^{\prime}(x)=\frac{\text{ 13}}{5}+\frac{32}{5(3x+1)} \\ T^{\prime}(x)=\text{ }\frac{dt(x)}{dx}(\frac{13}{5})+\frac{dt(x)}{dx}(\frac{32}{5(3x+1)} \\ T^{\prime}(x)=0+(\text{ -32\rparen\lparen}\frac{\frac{dt(x)}{dx}5(3x+1)^2}{\frac{dt(x)}{dx}(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ - 32\lparen}\frac{5(\frac{dt(x)}{dx}(3x+1)^2)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ -32\lparen}\frac{5(\frac{dt}{dx}(g)^2)(\frac{dt}{dx}(3x+1)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ -32\lparen}\frac{5(2g)(3)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ - 32\lparen}^\frac{5(2)(3x+1)(3)}{(5(3x+1)^2)^2} \\ T^{\prime}(x)=0\text{ -32\lparen}\frac{5\text{ x \lparen}2)(3x+1)(3)}{25(3x+1)^4} \\ T^{\prime}(x)=0\text{ - 32\lparen}\frac{2(3)}{5(3x+1)^3}) \\ T^{\prime}(x)=0\text{ - 32\lparen}\frac{6}{5(3x+1)^3}) \\ T^{\prime}(x)=\text{ - }\frac{192}{5(3x+1)^3} \\ T^{\prime}(1)=\text{ - }\frac{192}{5(3(1)+1)^3} \\ T^{\prime}(1)=\text{ - }\frac{192}{5(4)^3} \\ T^{\prime}(1)=\text{ - }\frac{192}{320} \\ T^{\prime}(1)=\frac{\text{ - 3}}{5} \end{gathered}[/tex]