On solving the question, we got that - The dimensions of the rug should be 18 feet and 24 feet
What is area of rectangle?By multiplying the rectangle's length by its breadth, we may get its area.
Equiangular quadrilaterals, like rectangles, are known in this way. This is so because a rectangle is a four-sided quadrilateral shape with parallel sides that are equal to one another and four corners with 90o angles. Rectangles are sometimes known as equiangular quadrilaterals since all of its angles are 90 degrees.
the parameters provided;
The room is 20 feet by 26 feet in size.
432 feet2 is the largest area rug she can afford.
If the floor will be a uniform stripe around the rug, then each dimension should have its uniform extra length of floor = (y).
[tex]Area = Length X Width\\432 = ((20=y) X (26-y)\\432 = 520 - 20y - 26y + y^2\\y^2 - 46y+88=0\\[/tex]
here, a= 1, b= -46, c =88
[tex]y = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\[/tex]
[tex]y = \frac{-(-46) +/- \sqrt{(-46)^2 - 4X1X88} } {2} \\\\y = 44 \\or\\ y = 2[/tex]
Therefore, Length = 20-2 = 18 ft
and width = 26-2 = 24ft
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a shirt was discountef from 75$ to 60$ what is the percent the shirt was reduced
Answer: 20%
Step-by-step explanation:
60 divided by 75 then times 100 = 80%
100% - 80% = 20%
A square floor is tiled, as partially shown, with a large number of regular hexagonal tiles. The tiles are colored blue or white. Each blue tile is surrounded by 6 white tiles and each white tile is surrounded by 3 white and 3 blue tiles. Ignoring part tiles, the ratio of the number of blue tiles to the number of white tiles is closest to_________.
A. 3:10 B. 1:4 C. 2:3 D. 1:2
Which of the following values is not an irrational number?
80, 7, 2.87, √59
80, 7, and 2.87 are not irrational numbers.
What is an irrational number?
An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, etc all are irrational.
Given numbers: 80, 7, 2.87, √59
80 = It is a rational number
7 = It is a rational number
2.87 = It is a rational number
√59 = It is an irrational number.
Hence, 80, 7, and 2.87 are not irrational numbers.
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What is the solution set for the equation |2y+3 | +2 = 15?
Answer:
y=5,-8
Step-by-step explanation:
Answer: hope this helps ♡
y = 5, y = -8
Step-by-step explanation:
∣2y + 3∣ + 2 = 15
∣2y + 3∣ + 2 - 2 = 15 - 2
∣2y + 3∣ = 13, ∣2y + 3∣ = -13
∣2y + 3 - 3∣ = 13 -3, ∣2y + 3 - 3∣ = -13 - 3
2y = 10, 2y = -16
y = 5, y = -8
Which system of equations is represented by the graph?
A. Y=x^2+4x
Y=-x^2+x+12
B. Y=x^2-8
Y=-x^2+16
C. Y=x^2
Y=-x^2-x-16
D. Y=x^2+8
Y=-x^2+16
Answer:
D
Step-by-step explanation:
Since we know that both parabolas are on the y-axis, it can't be A or C.
We also know they are above (0,0), so it can't be option B.
That leaves option D.
15(x+2)=60+9x welp I also need help
1… 1f21: 7: 4: 3a + 1 then what is 4th proportional?
B.
(8)
C
9
4
3
D.
3/4
1
9
2-Range of the data 112, 121, 184, 189, 177,190 is:
A.78 B.77 c 70 D.74
The 4th proportional of the given ratio is 4/3. option C
The range of the data 112, 121, 184, 189, 177, 190 is 78. option A
How to find 4th proportional?It follows from the concept of proportions that the ratios can be represented as follows;
21 : 7 = 4 : 3a + 1
21/7 = 4 / (3a + 1)
cross product
21 × (3a + 1) = 4 × 7
63a + 21 = 28
subtract 21 from both sides
63a = 28 - 21
63a = 7
a = 7/63
a = 1/9
So,
3a + 1
= 3(1/9) + 1
= 3/9 + 1
= 1/3 + 1
= 1 ⅓
= 4/3
21 : 7 = 4 : 4/3
Range of the data:
112, 121, 184, 189, 177, 190
Recall, the range of a dataset is the difference between the maximum and minimum data values and hence, we have;
Range = Highest data value - Lowest data value
= 190 - 112
= 78
Therefore, the range of the given set of data is 78.
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Which constant must she add to both sides of the equation so that the left side is a perfect square?
The constant that must be added to both sides of the equation to find the perfect square is b/2a.
What is the quadratic equation?The 2nd equation in x is known as a quadratic function. Ax2 + Bx + c = 0 is the quadratic equation in standard form, wherein there a and b are the coefficient, x is the constant, and c is the constant.
The presence of a non-zero component in the coefficient of x2 (a ≠ 0) is the first prerequisite for an expression to be a quadratic equation.
As per the given information in the question,
The equation for the quadratic equation is,
Ax² + Bx + c = 0
And for finding the roots,
d = b² - 4ac
Then, use the formula (-b±√d)/2a.
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Based on this projection, which of the following is closest to the number of t-shirts Marcus needs to sell during the first month to meet his goal? (100 brainley points plsss help)
Answer:
A. 1,500
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]
The given scenario can be modelled as a geometric series.
If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:
Sum Sₙ = 15,000n = 6If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:
r = (1 + 0.2) = 1.2Substitute these values into the formula and solve for a:
[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]
[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]
[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]
[tex]\implies a=1510.586188[/tex]
Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.
Check:
Month 1 = 1511Month 2 = 1511 × 1.2 = 1813Month 3 = 1813 × 1.2 = 2176Month 4 = 2176 × 1.2 = 2611Month 5 = 2611 × 1.2 = 3133Month 6 = 3133 × 1.2 = 3760Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004
Check:
Month 1 = 1500Month 2 = 1500 × 1.2 = 1800Month 3 = 1800 × 1.2 = 2160Month 4 = 2160 × 1.2 = 2592Month 5 = 2592 × 1.2 = 3110Month 6 = 3110 × 1.2 = 3732Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000
if each side is increased by 50℅.then find the increase percentage in its surface area
Answer:
Formula used:The surface area of cube = 6 side2
Calculation:According to the question,
Let the side of the cube be x
Each side of the cube increased by 50%.
= x(100 + 50)/100 = 1.5x
The surface area of the cube
⇒6x²
The new surface area of the cube (side = 1.5x)
⇒ 6 × 2.25x²
Increase percentage in the surface area
⇒((6 x 2.25 x²-6x²)/6 x² }× 100
⇒ 125%
The percentage increase in the surface area is 125%.The numbers x,y and z are given by x =[tex]\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} } , y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} } and z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex] . What is the value of x,y and z
The values of the expressions are x = √6, y = 2√3 and z = √2
How to evaluate the expressions?From the question, we have the following parameters that can be used in our computation:
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
We have
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
Take the square of both sides
So, we have
[tex]x^2 =12-3\sqrt{7} + 12 + 3\sqrt{7} - 2(\sqrt{12-3\sqrt{7} } * \sqrt{12 + 3\sqrt{7} })[/tex]
This gives
x² = 12 - 3√7 + 12 + 3√7 - 2√81
Evaluate the roots
So, we have
x² = 12 - 3√7 + 12 + 3√7 - 18
Evaluate the sum and the difference
x² = 6
Take the square roots of both sides
x = √6
Using the same steps above, we have
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
Square both sides
So, we have
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * \sqrt{7-4\sqrt{3 } } * \sqrt{7 + 4\sqrt{3} }[/tex]
This gives
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * 1[/tex]
Evaluate
y² = 12
Take the square root of both sides
y = 2√3
Lastly, we have
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
Square both sides
[tex]z^2 = 2 + \sqrt 3 + 2- \sqrt 3 - 2 * \sqrt{2 + \sqrt{3} } * \sqrt{2 - \sqrt{3} }[/tex]
This gives
z² = 4 - 2 *1
Evaluate
z = √2
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Write the equation of the line...
through: (-3, 1) with slope: 2
y = mx + b
Answer:
Step-by-step explanation:
Step 1: Use point-slope form and substitute in the x and y values
y-y1=m(x-x1)
y-(1)=2(x-(-3))
Step 2: Simplify the expression
y-1 = 2(x+3)
Add one to the other side
y= 2(x+3)+1
Multiple 2 by (x+3)
y=2x+6+1
Add common terms
y=2x + 7
If $42,400 is invested at an interest rate of 6% per year, find the value of the investment at the end of 5 years if interest is compounded annually, semiannually, monthly, daily, or continuously. Round to the nearest cent.
Annual=
Semiannual=
Monthly=
Daily=
Continuously=
The required values of the compound amount are $56740.76, $56982.05, $57191.25, $57232.60 and $57234.01 respectively.
What is compound interest?
Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has already accrued over the course of prior periods are used to calculate compound interest.
Given, Principal (P) = $42,400
interest rate(r) = 6% per year = 0.06
time(t) = 5 years
The compound amount is given by
[tex]A = P(1+\frac{r}{t} )^{nt}[/tex]
For compounded annually, n=1
[tex]A = 42400(1+0.06)^{1*5}[/tex] = $56740.76
For compounded semi-annually, n=2
[tex]A = 42400(1+\frac{0.06}{2})^{2*5}[/tex] = $56982.05
For compounded monthly, n=12
[tex]A = 42400(1+\frac{0.06}{12})^{12*5}[/tex] = $57191.25
For compounded daily, n=365
[tex]A = 42400(1+\frac{0.06}{365})^{365*5}[/tex] = $57232.60
For compounded continuously,
[tex]A=Pe^{rt} = 42400e^{0.06*5}[/tex] = $57234.01
Hence, these are the required values of the compound amount.
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The
approximate average distances from
the sun to Venus and Mercury are listed
below:
Venus: 1.08 x 108 kilometers
Mercury: 5.79 × 107 kilometers
How much closer to the sun is Mercury?
Express your answer using scientific
notation.
The subtraction of significant figures between the distance is 5.01 × 10⁷km
SubtractionIn this problem, we have to subtract the difference between the distance of Venus and Mercury. When subtracting significant digits, the amount of significant digits that will be in the final answer is determined by the number of significant digits present after the decimal place in the numbers we are subtracting.
The distance between Venus and Mercury can be calculated as
1.08 × 10⁸ - 5.79 × 10⁷ = 50,100,000km
To express the value in significant figures, we will have
50,100,000 = 5.01 × 10⁷km
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The population of a city is 4786000 in 1980. In 1990 the population had increased by 1.5%. What was the population in the year 2000 if it increased a further 1.2% from 1990 (in whole people)?
Answer:
4 916 083
Step-by-step explanation:
population in 1990
1.5 : 100 = x : 4 786 000
x = 1.5 · 4 786 000 / 100
x = 1.5 · 47 860
x = 71 790
4 786 000 + 71 790 = 4 857 790
population in 2000
1.2 : 100 = x : 4 857 790
x = 1.2 · 4 857 790 / 100
x = 0.012 · 4 857 790
x = 58 293.48
4 857 790 + 58 293.48 = 4 916 083.48
write an equation involving absolute value for each graph 24-29
Answer:
Step-by-step explanation:
24-29=-5
using the number line:)
Answer:
4-23=4b
Step-by-step explanation:
Terrence signed up for the Safe Venture driving school. He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes. When Terrence completes the 26 total hours of instruction, he will take his driver's test.
Which equation can you use to find w, the number of weeks the driving classes last?
The equation is 2w + 10 = 26.
The number of weeks the driving class lasts is 8 weeks.
With that,
Terrence signed up for the Safe Venture driving school.
He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.
When Terrence completes the 26 total hours of instruction, he will take his driver's test.
We have to determine,
Which equation can you use to find w, the number of weeks the driving class lasts.
According to the question,
He will spend 10 hours driving with an instructor and will also attend weekly 2-hour classes.
Then, The equation of the number of weeks the driving class lasts,
= 2w + 10
When Terrence completes the 26 total hours of instruction, he will take his driver's test.
2w + 10 = 26
He spends 10 hours driving and adding on 2 more classes with a total of 26 hours.
Therefore,
The number of weeks the driving class lasts,
2W + 10 = 26
2W = 26 - 10
2W = 16
W = (16/2)
W = 8
Hence, The number of weeks the driving class lasts is 8 weeks.
what is the p-value for testing if the color brightness of fuji film is significantly higher than the average of the other two brands?
Value of contrast given is 4.043 , standard error is 1.4535 and t is 2.782 So ,after analyzing this given data , the value for p for null hypothesis testing is 0.008
In Hypothesis Testing, the P-value method is used to determine the significance of the given null hypothesis. The decision to reject or support it is then made on the basis of the specified significance level or threshold.
This method computes a P-value, which is a test statistic. This statistic can tell us how likely it is that we will find a value (sample mean) that is as far away as the population mean.
P-value is an abbreviation for Probability.
We reject or fail to reject the null hypothesis based on that probability and a significance level.
In general, the lower the p-value, the greater the likelihood of rejecting the null hypothesis, and vice versa.
We also use the Z-table to complete this process.
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i need help with this
The scale factor of Dilation is 2
How to to calculate the scale factor of Trapezoid of QRST?The ratio of the scale of an original object to a new object that is a representation of it but is a different size is known as a scale factor.
We want to find the scale factor at which QRST is dilated to form Q'R'S'T'
We will find that the scale factor is 2.
In a general dilation, we will see that all the measures change in the same way, by the scale factor.
This means that:
QR*k = Q'R'
RS*k = R'S'
And so on, where k is the scale factor.
Then we can just find one of the equivalent measures in both trapezoids and find the value of k.
For example, we have:
Q'R' = 8
QR = 4
Replacing these on the above equation we get:
4*k = 8
k = 8/4 = 2
k = 2
Therefore the scale factor of dilation is 2.
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Regina spent $45.50 over 61/2 months on music downloads. If she spent the same amount of money each month, how much money, in dollars, did Regina spend per month on music downlo
Answer:
She spend $7 a month on downloads.
Step-by-step explanation:
y = the total spent on downloads
x = number of months
m = the amount spent each month
y = mx
45.50 = m(6.5) Divide both sides by 6.5
7 = m
(78000/ 19110) x100=
Answer:
= 408.16 or =20000/49
Step-by-step explanation:
= (78000/ 19110) x100
= (200/49)*100
=20000/49
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x2 = 17.
The solution of the given quadratic equation is x = 1.37, - 1.37.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions .
Given quadratic equation:
9x² = 17
⇒ x² = (17 / 9)
⇒ x = ± √(17 / 9)
⇒ x = ± (√17) / 3
⇒ x = 1.37, - 1.37
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Iris wants to buy a necklace. The necklace is
$70.00. She has a coupon for 20% off her entire
order. What is the sale price for the necklace
Answer:56
Step-by-step explanation:20% of 70 is 14 dollars so you have to subtract 70-14=56.
50 POINTS! PLEASE HURRY!
If you move the quadratic parent function, f(x) = x2, left 3 units, what is the equation of the new function?
g(x) = (x + 3)^2
g(x) = 3x^2
g(x) = x^2 - 3
g(x) = (x - 3)^2
The equation of the new function is: f(x) = (x- 3)²
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
The translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
We know that the function f(x+m) is equals to the function f(x) translated 'm' times to the left.
Therefore, to find the translate the function f(x) = x² twelve units to the right, we have given;
f(x- 3) = (x- 3)²
Therefore, the new function is: f(x) = (x- 3)²
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What is 7+x-1-5X simplified?
Answer:-4x + 6
Step-by-step explanation:
7 + x - 1 - 5x
6 - 4x
The answer is -4x +6
question content area top part 1 a statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. find the probability that a given class period runs between 50.5 and 51.25 minutes
The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.
Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.
The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.
[tex]P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15[/tex]
P = 0.15 means that the probability is 15%.
Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.
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PLEASE HELP ME BRAINLIEST IS THE REWARD
Answer:
13.3=c
Step-by-step explanation:
The hypotenuse can be found with the equation [tex]a^2+b^2=c^2[/tex]. For this problem, let
a=8.3
b=10.4
So,
[tex](8.3)^2+(10.4)^2=c^2\\177.05=c^2\\\sqrt{177.05}=\sqrt{c^2}\\13.31=c[/tex]
#12: If the slope of a linear function is m = 6/5, how much
does the output change, when the input is decreased by 30?
The output changes by:
By using unitary method, it can be calculated that
When input decreases by 30, output decreases by 36
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
This is a problem on unitary method
Slope = [tex]\frac{6}{5}\\[/tex]
When input decrease by 5, output decreases by 6
When input decrease by 1, output decreases by [tex]\frac{6}{5}[/tex]
When input decreases by 30, output decreases by [tex]\frac{6}{5} \times 30[/tex]
When input decreases by 30, output decreases by 36
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Ccss math 7 unit 7. agles, triangles, ad prisms find the measure of all the missing anges. please help with all the answers its due tomorrow !!!
Since a + b + c are vertically opposite angles, e = 130.
What are angles?When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.
When two lines meet at a point, an angle is created.
An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.
The circularity or rotation of an angle is often measured in degrees and radians.
Angles are a common occurrence in daily life.
Angles are used by engineers and architects to create highways, structures, and sports venues.
According to our question-
d=70, opposite vertical angle
180 - 70 - 40 = 2 using angles on a straight line.
We now possess the two angles, and since they are perpendicular to one another, a and c = 35.
Because of the vertically opposed angles, b = 40.
4. Because 90-70, a=30.
Because an is 30, divide 90 by 30 to obtain b, 70.
vertically opposite angles, d=70
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I know that in my time signature, I want a quarter note to get the beat and I want the four beats in each measure. What number should I have in the bottom of my time signature? What number should I put in the top of my time signature?
4/4 is the most commonly used time signature. You will have 4 beats per measure and the quarter note will be one beat.
What is time signature?Two numbers make up a time signature, which is similar to a fraction. The time signature may alter throughout a work, but it always appears at the beginning. The bottom number is the note value that corresponds to one beat, and the top number is the number of beats in a measure. A song in 4/4 time, for instance, will have four quarter notes every measure, whereas a song in 9/8 time will have nine eighth notes per measure.
Here,
The most popular time signature is 4/4. The quarter note is one beat, and each measure has four beats.
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