The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.
Since the length is labeled 2 inches, the real length of the room is:
[tex]2in\times30=60in[/tex]Since the width is labeled 4.5 inches, the real with of the room is:
[tex]4.5in\times30=135in[/tex]1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:
[tex]\begin{gathered} 60in=60in\times\frac{1ft}{12in}=5ft \\ \\ 135in=135in\times\frac{1ft}{12in}=11.25ft \end{gathered}[/tex]Multiply the width and the length to find the area of the room:
[tex]A=(5ft)(11.25ft)=56.25ft^2\approx56ft^2[/tex]Therefore, to the nearest whole number, the area of the game room is 56ft^2.
A game fair requires that you draw a queen from a deck of 52 ards to win. The cards are put back into the deck after each draw, and the deck is shuffled. That is the probability that it takes you less than four turns to win?
The probability (P) is winning in less than four turns can be decomposed as the following sum:
The probability of winning in one turn is
[tex]P(\text{Winning in turn 1})=\frac{\#Queens}{\#Cards}=\frac{4}{52}.[/tex]The probability of winning in the second turn is
[tex]\begin{gathered} P(\text{ Winning in the second turn})=P(\text{ Lossing (in turn 1)})\cdot P(\text{ Winning (in turn 2)}), \\ \\ P(\text{ Winning in the second turn})=\frac{\#NoQueens}{\#Cards}\cdot\frac{\#Queens}{\#Cards}, \\ \\ P(\text{ Winning in the second turn})=\frac{48}{52}\cdot\frac{4}{52}\text{.} \end{gathered}[/tex]The probability of winning in the third turn is
[tex]\begin{gathered} P(\text{ Winning in the third turn})=P(\text{ Lossing (in turn 1)})\cdot P(\text{ Lossing (in turn 2)})\cdot P(\text{ winning (in turn 3)}), \\ \\ P(\text{ Winning in the third turn})=\frac{\#NoQueens}{\#Cards}\cdot\frac{\#NoQueens}{\#Cards}\cdot\frac{\#Queens}{\#Cards}, \\ \\ P(\text{ Winning in the third turn})=\frac{48}{52}\cdot\frac{48}{52}\cdot\frac{4}{52}\text{.} \end{gathered}[/tex]Adding all together, we get
[tex]\begin{gathered} P(\text{ Winning in less than four turns})=\frac{4}{52}+\frac{48}{52}\cdot\frac{4}{52}+\frac{48}{52}\cdot\frac{48}{52}\cdot\frac{4}{52}, \\ \\ P(\text{ Winning in less than four turns})=\frac{469}{2197}, \\ \\ P(\text{ Winning in less than four turns})\approx0.2135, \\ \\ P(\text{ Winning in less than four turns})\approx21.35\% \end{gathered}[/tex]AnswerThe probability of winning in less than four turns is (approximately) 21.35%.
Shaun deposits $3,000 into an account that has an rate of 2.9% compounded continuously. How much is in the account after 2 years and 9 months?
The formula for finding amount in an investment that involves compound interest is
[tex]A=Pe^{it}[/tex]Where
A is the future value
P is the present value
i is the interest rate
t is the time in years
e is a constant for natural value
From the question, it can be found that
[tex]\begin{gathered} P=\text{ \$3000} \\ i=2\frac{9}{12}years=2\frac{3}{4}years=2.75years \end{gathered}[/tex][tex]\begin{gathered} e=2.7183 \\ i=2.9\text{ \%=}\frac{2.9}{100}=0.029 \end{gathered}[/tex]Let us substitute all the given into the formula as below
[tex]A=3000\times e^{0.29\times2.75}[/tex][tex]\begin{gathered} A=3000\times2.21999586 \\ A=6659.987581 \end{gathered}[/tex]Hence, the amount in the account after 2 years and 9 months is $6659.99
69=2g-24 I NEED TO FIND G
A house has increased in value by 35% since it was purchased. If the current value is S432,000, what was the value when it was purchased?
The value of the house when it was purchased = $32000
Explanation:The original percentage value = 100%
The current percentage value = 100% + 35% = 135%
Current value = $432000
Original value = x
[tex]\begin{gathered} The\text{ current value =}\frac{135}{100}\times The\text{ original value} \\ \\ 432000=1.35\times x \\ \\ x=\frac{432000}{1.35} \\ \\ x=$ 320000 $ \end{gathered}[/tex]The value of the house when it was purchased = $32000
A stock is worth $28,775 and drops 33% in one day. What percent does the stock have to grow the next day to get back to $28,775
ANSWER:
49.254%
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value after it has drops by 33%, like this:
[tex]\begin{gathered} 28775-28775\cdot33\% \\ \\ 28775-28775\cdot0.33 \\ \\ 28775-9495.75=19279.25 \end{gathered}[/tex]Now, we calculate what should grow by the following equation:
[tex]\begin{gathered} 19279.25+19279.25\cdot \:x=28775\: \\ \\ x=\frac{28775\:-19279.25}{19279.25} \\ \\ x=\frac{9495.75}{19279.25} \\ \\ x=0.49254\cong49.254\% \end{gathered}[/tex]The percent that should grow is 49.254%
A polynomial function is given.
Q(x) = −x2(x2 − 9)
(a) Describe the end behavior of the polynomial function.
End behavior: y → as x → ∞
y → as x → −∞
The end behavior of the polynomial is:
y → −∞ as x → ∞
y → −∞ as x → −∞
How is the end behavior?Here we have the polynomial:
Q(x) = -x²*(x² - 9)
Remember that polynomials with even degrees have the same behavior for the negative values of x than for the positive, in this case if we expand the polynomial we get:
Q(x) = -x⁴ + 9x²
The leading coefficient is negative, then the end behavior will tend to negative infinity in both ends, then we get:
y → −∞ as x → ∞
y → −∞ as x → −∞
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Find the coordinates of the other endpoint of a segment with the given endpoint and Midpoint M.T(-8,-1)M(0,3)
If we have 2 endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint will be:
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Now, we know the coordinates of one endpoint (x1, y1) equal to (-8, -1) and the midpoint (x, y) equal to (0,3), so we can replace those values and solve for x2 and y2.
Then, for the x-coordinate, we get:
[tex]\begin{gathered} 0=\frac{-8+x_2}{2} \\ 0\cdot2=-8+x_2 \\ 0=-8+x_2 \\ 0+8=-8+x_2+8 \\ 8=x_2 \end{gathered}[/tex]At the same way, for the y-coordinate, we get:
[tex]\begin{gathered} 3=\frac{-1+y_2}{2} \\ 3\cdot2=-1+y_2 \\ 6=-1+y_2 \\ 6+1=-1+y_2+1 \\ 7=y_2 \end{gathered}[/tex]Therefore, the coordinates of the other endpoint are (8, 7)
Answer: (8, 7)
Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]Finding an output of a function from its graphThe graph of a function fis shown below.Find f (0).543-2f(0) =I need help with this math problem.
Given:
Given a graph of the function.
Required:
To find the value of f(0), by using graph.
Explanation:
From the given graph
[tex]f(0)=-4[/tex]Final Answer:
[tex]f(0)=-4[/tex]Solve the equation.k²=47ks.(Round to the nearest tenth as needed. Use a comma to separate answers as needed.
The initial equation is:
[tex]k^2=47[/tex]Then, we can solve it calculating the square root on both sides:
[tex]\begin{gathered} \sqrt[]{k^2}=\sqrt[]{47} \\ k=6.9 \\ or \\ k=-6.9 \end{gathered}[/tex]Therefore, k is equal to 6.9 or equal to -6.9
Answer: k = 6.9 or k = -6.9
find the equation of the axis of symmetry of the following parabola algebraically. y=x²-14x+45
Answer:
x = 7, y = -4
(7, -4)
Explanation:
Given the below quadratic equation;
[tex]y=x^2-14x+45[/tex]To find the equation of the axis of symmetry, we'll use the below formula;
[tex]x=\frac{-b}{2a}[/tex]If we compare the given equation with the standard form of a quadratic equation, y = ax^2 + bx + c, we can see that a = 1, b = -14, and c = 45.
So let's go ahead and substitute the above values into our equation of the axis of symmetry;
[tex]\begin{gathered} x=\frac{-(-14)}{2(1)} \\ =\frac{14}{2} \\ \therefore x=7 \end{gathered}[/tex]To find the y-coordinate, we have to substitute the value of x into our given equation;
[tex]\begin{gathered} y=7^2-14(7)+45 \\ =49-98+45 \\ \therefore y=-4 \end{gathered}[/tex]Use the slope and y-intercept to graph the line whose equation is given. 2 y = -x + 5x+1
ok
y = -2/5 + 1
This is the graph
2. What is the greatestcommon factor of12. 18, and 36?
The Solution:
Given the numbers below:
12, 18 and 36.
We are asked to find the greatest common factor of the above numbers.
Note:
Greatest Common Factor means Highest Common Factor (HCF).
Recall:
The Greatest common factor of 12, 18 and 36 is the highest number that can divide 12, 18 and 36 without any remainder.
Thus, the correct answer is 6.
if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
Question
Mrs. Hanson has a potato salad recipe that calls for 238 pounds of potatoes, but she wants to make 112 times as much as the recipe calls for.
The diagram represents the number of pounds of potatoes that Mrs. Hanson needs.
How many pounds of potatoes does Mrs. Hanson need?
Answer:
3 9/16 lbs
Step-by-step explanation:
need help. first correct answer gets brainliest plus 15 pts
We are given that lines V and 0 and lines C and E are parallel.
We are asked to prove that ∠15 and ∠3 are congruent (equal)
In the given figure, angles ∠3 and ∠7 are "corresponding angles" and they are equal.
[tex]\angle3=\angle7[/tex]In the given figure, angles ∠7 and ∠6 are "Vertically opposite angles" and they are equal.
[tex]\angle7=\angle6[/tex]Angles ∠6 and ∠14 are "corresponding angles" and they are equal.
[tex]\angle6=\angle14[/tex]Angles ∠14 and ∠15 are "Vertically opposite angles" and they are equal.
[tex]\angle14=\angle15[/tex]Therefore, the angles ∠15 and ∠3 are equal.
[tex]\angle3=\angle7=\angle6=\angle14=\angle15[/tex]Josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years?Round your answer to the nearest dollar.
The equation for the total amount after compounded interest is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}^{}[/tex]Where A is the final amount, P is the initial amount, r is the annual interest, n is how many times per year the interest is compounded and t is the time in years.
Since the interest is compounded annually, it is compounded only once per year, so
[tex]n=1[/tex]The other values are:
[tex]\begin{gathered} P=4400 \\ r=3.2\%=0.032 \\ t=12 \end{gathered}[/tex]So, substituteing these into the equation, we have:
[tex]\begin{gathered} A=4400(1+\frac{0.032}{1})^{1\cdot12} \\ A=4400(1+0.032)^{12} \\ A=4400(1.032)^{12} \\ A=4400\cdot1.4593\ldots \\ A=6421.0942\ldots\approx6421 \end{gathered}[/tex]So, she will have approximately $6421.
Find an expression equivalent to the one shown below.913 x 9-6OA. 79OB.919OC. 97OD. 9-78
Answer:
C. 9⁷
Explanation:
We will use the following property of the exponents:
[tex]x^a\times x^b=x^{a+b}[/tex]It means that when we have the same base, we can simplify the expression by adding the exponents. So, in this case, the equivalent expression is:
[tex]9^{13}\times9^{-6}=9^{13-6}=9^7[/tex]Therefore, the answer is C. 9⁷
A baby cows growth. About how many pounds does the baby cow gain each week?
Growth per week = 124 - 122 = 126 - 124 = 2
. = 2 pounds + 1 pound additional
. = 3
Then answer is
OPTION B) 3 pounds
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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The cost to mail a package is 5.00. Noah has postcard stamps that are worth 0.34 and first-class stamps that are worth 0.49 each. An equation that represents this is 0.49f + 0.34p = 5.00Solve for f and p.If Noah puts 7 first-class stamps, how many postcard stamps will he need?
ANSWER
[tex]\begin{gathered} f=\frac{5.00-0.34p}{0.49} \\ p=\frac{5.00-0.49f}{0.34} \\ p=4.618\approx5\text{ postcard stamps} \end{gathered}[/tex]EXPLANATION
The equation that represents the situation is:
[tex]0.49f+0.34p=5.00[/tex]To solve for f, make f the subject of the formula from the equation:
[tex]\begin{gathered} 0.49f=5.00-0.34p \\ \Rightarrow f=\frac{5.00-0.34p}{0.49} \end{gathered}[/tex]To solve for p, make p the subject of the formula from the equation:
[tex]\begin{gathered} 0.34p=5.00-0.49f \\ \Rightarrow p=\frac{5.00-0.49f}{0.34} \end{gathered}[/tex]To find how many postcard stamps Noah will need if he puts 7 first-class stamps, solve for p when f is equal to 7.
That is:
[tex]\begin{gathered} p=\frac{5.00-(0.49\cdot7)}{0.34} \\ p=\frac{5.00-3.43}{0.34}=\frac{1.57}{0.34} \\ p=4.618\approx5\text{ postcard stamps} \end{gathered}[/tex]School: Practice & Problem Solving 7.1.PS-18 Question Help A rectangle and a parallelogram have the same base and the same height. How are their areas related? Provide an example to justify your answer The areas equal. A rectangle has dimensions 5 m by 7 m, so its area is m² A parallelogram with a base of 5 m and a height of 7 m has an area of (Type whole numbers.)
The image shown below shows the relationship between areas of rectangle and parallelogram
It can be seen that the areas are equal when they have the same sides or dimension
A rectangle has dimensions 5 m by 7 m, so its area is 5m x 7m = 35m²
A parallelogram with a base of 5 m and a height of 7 m has an area of 5m x 7m = 35m²
do you think you'd be able to help me with this
x = wz/y
Explanation:[tex]\frac{w}{x}=\frac{y}{z}[/tex]To solve for x, first we need to cross multiply:
[tex]w\times z\text{ = x }\times y[/tex]Now we make x the subject of the formula:
[tex]\begin{gathered} To\text{ make x stand alone, we n}ed\text{ to remove any other variable around x} \\ \text{divide both sides by y}\colon \\ \frac{w\times z}{y}\text{ =}\frac{\text{ x }\times y}{y} \end{gathered}[/tex][tex]x\text{ = }\frac{wz}{y}[/tex]find the simple interest earned, to the nearest cent, for each principal interest rate, and time.
Answer:
$8.40
Explanation:
From the given statement:
Principal = $840
Time = 6 Months
Rate = 2%
Note that Time must be in Years, therefore:
Time = 6 Months = 6/12 = 0.5 Years
[tex]\begin{gathered} \text{Simple Interest }=P\times R\times T \\ =840\times2\%\times0.5 \\ =840\times0.02\times0.5 \\ =\$8.40 \end{gathered}[/tex]The simple interest earned is $8.40
Jackson purchased a pack of game cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the oeiginal price of the card.. Wrote an expression that can be used to determine the final cost of the cards.
Given:
Discount - 22% = 0.22
Sales Tax - 6% = 0.06
Required:
Expression for the final cost of the cards, x
Solution:
Let: y represent the original price of the card.
x represent the final cost of the cards
D represent the discounted cost of the cards
Assume that the the sales tax is applied to the price after the discount.
D= Original Price ( 1 - Discount) = y ( 1 - 0.22) = 0.78y
To compute for the final cost,
Final Cost = D + Tax
Tax = 0.06 D
x = D + 0.6(D)
x = 1.06D
x = 1.06 ( 0.78 y)
x = 0.827y
Answer:
The final cost of the card can be describe by the expression:
x = 0.827y
(Algebra 1 Equivalent equations)
In a family, the middle child is 5 years older than the youngest child.
Tyler thinks the relationship between the ages of the ages of the children can be described with 2m-2y=10, where m is the age of the middle child and y is the age of the youngest.
Explain why Tyler is right.
Let the middle child is m and youngest is y.
The middle child is 5 years older than the youngest child, it can be shown as:
m - y = 5Tyler's equation is equivalent to ours since it can be obtained by multiplying both sides of our equation by 2:
2(m - y) = 2*52m - 2y = 10 ⇔ m - y = 5So Tyler is right.
Use Vocabulary in Writing 9. Explain how you can find the product 4 X 2 and the product 8 X 2 Use at least 3 terms from the Word List in your explanation.
Okay, here we have this:
Find all solutions in[0, 2pi): 2sin(x) – sin (2x) = 0
Based on the answer choices, replace the pair of given values and verify the equation, as follow:
For x = π/4, π/6
[tex]2\sin (\frac{\pi}{4})-\sin (\frac{2\pi}{4})=2\frac{\sqrt[]{2}}{2}-1\ne0[/tex]the previous result means that the given values of x are not solution. The answer must be equal to zero.
Next, for x = 0, π
[tex]\begin{gathered} 2\sin (\pi)-\sin (2\pi)=0-0=0 \\ 2\sin (0)-\sin (0)=0-0=0 \end{gathered}[/tex]For both values of x the question is verified.
The rest of the options include π/4 and π/3 as argument, you have already shown that these values of x are not solution.
Hence, the solutions for the given equation are x = 0 and π
A rectangular room is 1.5 times as long as it is wide, and its perimeter is 26 meters. Find the dimension of the room.The length is :The width is :
The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"
The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:
[tex]P=2w+2l[/tex]We know that:
P=26m
w=x
l=1.5x
Then, replace the measurements on the formula:
[tex]\begin{gathered} 26=2x+2\cdot1.5x \\ 26=2x+3x \end{gathered}[/tex]From this expression, you can calculate x, first, add the like terms:
[tex]26=5x[/tex]Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{26}{5}=\frac{5x}{5} \\ 5.2=x \end{gathered}[/tex]The width is x= 5.2m
The length is 1.5x= 1.5*5.2= 7.8m
Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 35 students from this distribution.
What is the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars? Round to five decimal places
The probability that an SRS of 35 students will spend an average o between 600 and 700 dollars is 98.61%
Given,
The mean of the normal distribution, μ = 650
Standard deviation of the distribution, σ = 120
n = 35
By using central limit theorem, standard deviation for SRS of n, δ = σ/√n = 120/√35
The z score = (x - μ) / σ
By using central limit theorem,
z score = (x - μ) / δ
Here,
We have to find the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars:
(p value of z score of x = 700) - (p value of z score of x = 600)
z score of x = 700
z = (x - μ) / δ = (700 - 650) /( 120/√35) = (50 × √35) / 120 = 2.46
p value of z score 2.46 is 0.99305
z score of x = 600
z = (x - μ) / δ = (600 - 650) /( 120/√35) = (-50 × √35) / 120 = -2.46
p value of z score -2.46 is 0.0069469
Now,
0.99305 - 0.0069469 = 0.9861031 = 98.61%
That is, the probability that an SRS of 35 students will spend an average o between 600 and 700 dollars is 98.61%
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