Hence, the correct option is C: x=5
students at a local school were asked. “about how many hours do you spend on homework each week “?The table shows the results of the survey . classify the statement below as true or false .more students study for 5 to 6 hours than for 1 to 2 hours
From the table:
The number of students that study for 5 to 6 hours = 109
The number of students that study for 1 to 2 hours = 142
Since 109 is less than 142:
The statement is False because 109 students study for 5 to 6 hours and 142 students study for 1 to 2 hours.
Pure acid is to be added to a 20% acid solution to obtain 44 L of a 40% acid solution.What amounts of each should be used?
Let:
x be the liters of 20% acid solution.
y be the liters of pure acid solution.
To find x and y, follow the steps below.
Step 01: Write an equation for the number of liters.
The number of liters of the solution is 44, which is the sum of x and y.
[tex]x+y=44[/tex]Step 02: Isolate y in the equation above.
To do it, subtract x from both sides.
[tex]\begin{gathered} x+y-x=44-x \\ y=44-x \end{gathered}[/tex]Step 03: Write an equation that expresses the total of acid.
The total of acid is 0.4*44, which is equal to 1y plus 0.2x.
[tex]\begin{gathered} 0.4\cdot44=1\cdot y+0.2\cdot x \\ 17.6=y+0.2x \end{gathered}[/tex]Step 04: Substitute y by 44 - x in the equation above and isolate x.
[tex]\begin{gathered} 17.6=44-x+0.2x \\ 17.6=44-0.8x \end{gathered}[/tex]To isolate x, subtract 44 from both sides.
[tex]\begin{gathered} 17.6-44=44-0.8x-44 \\ -26.4=-0.8x \\ \end{gathered}[/tex]Now, divide both sides by -0.8.
[tex]\begin{gathered} \frac{-26.4}{-0.8}=\frac{-0.8}{-0.8}x \\ 33=x \end{gathered}[/tex]Step 05: Use the equation from step 2 to find y.
[tex]\begin{gathered} y=44-x \\ y=44-33 \\ y=11 \end{gathered}[/tex]Answer:
x is the liters of 20% acid solution = 33 L.
y is the liters of pure acid solution = 11 L.
In which quadrant, or on which axis, does the terminal side of angle (- 100straight pi) lie?
The given angle is
[tex]\theta=-\frac{100}{\pi}[/tex]First, we have to transform this angle into degrees. We know pi=180°, so
[tex]\theta=-\frac{100}{180}=-\frac{50}{90}=-\frac{5}{9}=-0.56[/tex]The given angle is placed on the first quadrant.Assuming that the angle is starting on the positive x-axis.
question will be in picture
Consider the guven system of equations,
[tex]\begin{gathered} x-y=-1 \\ 2x+y=4 \end{gathered}[/tex]It is asked to find the correct graph which represent the solution of this system.
Logic: Find the solution and see which graph gives the same solution.
Add the equations,
[tex]\begin{gathered} (x-y)+(2x+y)=-1+4 \\ 3x+3 \\ x=1 \end{gathered}[/tex]Substitute this value in the first equation,
[tex]\begin{gathered} 1-y=-1 \\ y=1+1 \\ y=2 \end{gathered}[/tex]Thus, the given system has a unique solution (1,2).
Now, observe that only the graph given in option (c) shows the line intersecting at point (1,2).
Therefore, option (c) is the correct choice.
J is the midpoint of HK, H has coordinates (5,-3), and J has coordinates (7,3). Find the coordinates of K.The coordinates of K are
Answer:
The coordinates of K is;
[tex](9,9)[/tex]Explanation:
We want to find the coordinates of point K.
Given that J is the midpoint of HK and;
H has coordinates (5,-3)
J has coordinates (7,3).
The formula for calculating midpoint is;
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]where x1 and x2 are the x coordinates of the endpoints and y1 and y2 are the y coordinates of the endpoints.
To get the coordinates of one of the endpoints, we have;
[tex]\begin{gathered} x_2=2x-x_1 \\ y_2=2y-y_1 \end{gathered}[/tex]substituting the given coordinates of the mid point and endpoint;
[tex]\begin{gathered} x_2=2(7)-5 \\ x_2=14-5 \\ x_2=9 \end{gathered}[/tex][tex]\begin{gathered} y_2=2(3)-(-3) \\ y_2=6+3 \\ y_2=9 \end{gathered}[/tex]Therefore, the coordinates of K is;
[tex](9,9)[/tex]Write the ratio as a fraction in simplest form without any units.9 gallons to 28 quarts
Given
The ratio, 9 gallons to 28 quarts.
To find:
The ratio as a fraction in lowest term.
Explanation:
It is given that,
The ratio, 9 gallons to 28 quarts.
That implies,
[tex]\begin{gathered} 9\text{ }gallons\text{ }to\text{ }28\text{ }quarts=\frac{9\text{ }gallons}{28\text{ }quarts} \\ =\frac{9\times4\text{ }quarts}{28\text{ }quarts} \\ =\frac{9}{7} \end{gathered}[/tex]Hence, the simplest form of the ratio is 9/7.
Solve for t and graph the solution.|t+ 4| < 2
The solution to the inequality is (-6, -2). The graph of the solution is attached below.
We are given an inequality. The inequality consists of a variable "t" and it also uses the modulus function. A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. The inequality is |t + 4| < 2. We can solve the inequality by expanding the modulus operator. The inequality becomes -2 < (t + 4) < 2. Now we will subtract 4 from all the sides in the inequality. The inequality is solved as -6 < t < -2. The interval notation for the solution is (-6, -2). The graph is attached below.
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Side PV measures 35 meters. Find the value of VT rounded to thenearest tenth if necessary.
By definition,
sin(angle) = opposite/hypotenuse
From the picture,
sin(60°) = VT/PV
√3/2 = VT/35
√3/2*35 = VT
30.3 meters = VT
The note A has a frequency of 1,760 hertz. The note D has a period of 1,175 hertz. Find theratio of A to D to two decimal places. Express the answer in integer ratio form.
Ratios
Note A has a frequency of
fa=1,760 Hz
Note D has a period of 1,175 hertz
(the previous data should be frequency, not period)
We are required to find the ratio of A to D. Let's call it r:
[tex]r=\frac{1,760^{\prime}}{1,175}[/tex]Dividing: r = 1.4978. Rounding to two decimal places:
r = 1.50
Now to express the answer in integer ratio form, we need to simplify the fraction.
First, we divide by 5 up and down:
[tex]r=\frac{352^{\prime}}{235}[/tex]There are no more common divisors for both numbers, thus the integer ratio form is r = 352/235
if y=3x+4 and y=2x+8, find the value of both x and y.
having that x=4, we get that
[tex]y=2\cdot4+8=16[/tex]Write a recursive sequence that represents the sequence defined by the following explicit formula: an=-405(-1/3)^n+1
ok
[tex]\begin{gathered} \text{ an = -405(-}\frac{1}{3})^{n\text{ + 1 - 1}} \\ \text{ an = -405(-}\frac{1}{3})^n \end{gathered}[/tex]
I need help with this
Ok, so
We have the following expression:
We're going to multiply all terms inside the bracket by "-x", and we obtain:
So, the answer is B.
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 1: Problem
Over the summer, Audrey had a job and earned $528. She spent $125.70 on a new bike and $85.09 for some new clothes. How much money does Audrey have left?
Step 2: Concept
Word problem on subtraction
Step 3: Method
Audrey total earning = $528
Money spent on new bike = $125.7
Money spent on new clothes = $85.09
Money left = 528 - 125.7 - 85.09
= $317.21
Step 4: Final answer
Audrey money left = $317.21
Simplify each expression using Product to a Power Property a. (9a)^2 b. ( 3x)^2
1) Let's simplify those expressions making use of exponents rules:
[tex](9a)^2=81a^2[/tex]Note that the exponent outside the parenthesis is 'distributed' over each term inside.
2) Similarly for the second expression we can state that:
[tex](3x)^2=9x^2[/tex]Cyrus is hosting a dinner to celebrate Nowruz, the Perian New Year. His groceries cost $150 before he uses a 10% off coupon. He also order $50 worth of flowers Sales tax on the flowers in 6.254%. What is the total amount Cyrus spends?
Data:
Groceries: $150
10% off
Flowers: $50
Sales tax on the flowers: 6.254%
To find the total amount:
1. Find the 10% of 150:
[tex]150\cdot\frac{10}{100}=15[/tex]2. As the coupon is 10% off you substract the 10% of $150:
[tex]150-15=135[/tex]For the groceries Cyrus pays $135
3. Find the 6.254% of 50:
[tex]50\cdot\frac{6.254}{100}=3.13[/tex]4. As the 6.254% is sales tax you add it to the $50:
[tex]50+3.127=53.13[/tex]For the flowers Cyrus pays $53.13
The total amount Cyrus spends is: $188.13[tex]135+53.127=188.13[/tex]Katherine is speeding in her car, and sees a parked police car on the side of the road right next to her at t=0 seconds. She immediately decelerates, but the police car accelerates to catch up with her (assume the two cars are going in the same direction in parallel paths). The distance that Katherine has traveled in feet after t seconds can be modeled by the equation d(t) = 150 + 75t - 1.2t^2. The distance that the police car travels after t seconds can be modeled by the equation d(t) = 4t^2.a) How long will it take the police car to catch up to Katherine?b) How many feet has Katherine traveled from the time she saw the police car until the police car catches up to her?
When the police car catches up Katherine their distances from the point at t=0 are the same, then we can find the time that it takes them to advance that distance by making the expression that models the distance of Katherine and the equation for the distance of the police equal, like this:
[tex]\begin{gathered} 150+75t-1.2t^2=4t^2 \\ 150+75t-5.2t^2=0 \end{gathered}[/tex]We know that for an equation of the form at^2+bt+c=0 the value of t can be calculated with the quadratic formula, for this case a= -5.2, b=75 and c=150, then applying the quadratic formula we get:
[tex]undefined[/tex]selecting among the numbers 1 through 8 and repeating none of them, fill in the boxes below to make the sum as close as possible to one but not equal to one
We need ti fill in the boxes below, selecting among the numbers 1 through 8 and repeating none of them to make the sum as close as possible to 1 but not equal to 1.
First fraction could be 1/2
Now, the second fraction should be closer to 1/2 to make the sum as close as possible to 1, but not equal to 1.
We know that 3/6 = 1/2
So, 3/7 would be closer to 1/2
Therefore, the boxes could be filled as;
[tex]\frac{1}{2}+\frac{3}{7}[/tex]..
Sketch a quick diagram of how all the quadrilaterals relate to one another
The diagram of various types of quadrilaterals are attached below.
A quadrilateral is polygon that has 4 sides.
Firstly we have a parallelogram which has both pairs of opposite side equal and parallel.
Second we have a trapezium where only one pair of side is parallels but other pair is not parallel.
A rhombus is a parallelogram whose all sides are equal but the angles are not right angles.
A rectangle has all angles 90° but the opposite sides are equal but adjacent sides are not equal.
A square has all sides equal and all angles 90° .
A kite has only 2 pairs of adjacent sides equal.
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Rose curves are characterized by equations of the form r=acos(nθ) or r=asin(nθ), a≠0. If n≠0 is even, the rose has __________ petals; if n≠±1 is odd, the rose has __________ petals.
We have that:
If n is an even integer, then the rose will have 2n petals.
If n is an odd integer, then the rose will have n petals.
Answer:
Rose curves are characterized by equations of the form r=acos(nθ) or r=asin(nθ), a≠0. If n≠0 is even, the rose has 2n petals; if n≠±1 is odd, the rose has n petals.
unsure about this one tried and couldn’t seem to figure it out
Given:
The figure contains the rectangle and half-circle.
The perimeter of the half-circle is,
[tex]\begin{gathered} \text{Half}-\text{circle}=\pi r+d \\ r=\frac{d}{2}=\frac{8}{2}=4 \\ \text{Half}-\text{circle}=\pi(4)+8 \\ =3.14\times4+8 \\ =20.56 \end{gathered}[/tex]The perimeter of the figure is,
[tex]P=10+8+10+20.56=48.56[/tex]Answer: P = 48.56 ft.
Challenge The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1996 his card was worth $9.17. The value has increased by $1.65 each year since then, Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2006? Express the relationship with an equation. y=?
$151.31. Not proportional.
y= 9.17 +1.65x
1) Gathering the data
1996 Retired $ 9.17
9.17(1.65)^x
2) Since the value of that card has been increasing 1.65 yearly, then we can write the following equation:
[tex]y=9.17+1.65x[/tex]For y= Value, and x =years
Let's find out the value of the card in 2006, i.e. 10 years later. Plug x=10 into the above function:
[tex]\begin{gathered} y=9.17+1.65x \\ y=9.17+1.65(10) \\ y=9.17+16.5 \\ y=151.305\approx y=151.31 \end{gathered}[/tex]3) Hence, the value of the card in 2006 is $151.31
(rounded off to the nearest hundredth)
And since the initial value is $9.17, then it is not a proportional relationship since an initial value of a proportional is always 0.
The total annual sales for Herman's Hardware Store was $1,246,135 and the total accounts receivable was $41,728. What was the average collection period to the nearestwhole day?12 days14 days18 days24 daysNone of these choices are correct.
The average collection Period formula is
[tex]\text{Average collection period=}\frac{Account\text{ receivable}}{\frac{Annual\text{ sales}}{365}}[/tex][tex]\begin{gathered} \text{Annual sales=\$1,246,135} \\ \text{Account receivable =\$41,728} \end{gathered}[/tex]Substitute the values above in the average collection period
[tex]\begin{gathered} \text{Average collection period =}\frac{41728}{\frac{1246135}{365}} \\ =\frac{41728}{3414.06} \\ =12.222 \\ \approx12days \end{gathered}[/tex]Hence the average collection period to the nearest whole day is 12 days
Question #10: A pizza restaurant sells a personal square pizza (5 inch side) for $4. What should the cost of a large square pizza (12 inch side) be, so that both pizzas cost the same amount per square inch?
The per square-inch cost of the first kind of pizza is $0.16 to maintain this ratio for 12-inch side pizza the cost must be $23.04.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
Cost of first pizza = $4
Area = 5 x 5 = 25 square inch
Per square cost = 4/25 = $0.16
With this ratio,
Cost of 12 inches side = 12 x 12 x 0.16 = $23.04
Hence "The per square-inch cost of the first kind of pizza is $0.16 to maintain this ratio for 12-inch side pizza the cost must be $23.04".
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what is (x + 5)(2× - 3) = 0 in expanded form??
(x + 5)(2x -3) = 0
2x² - 3x + 10x - 15 = 0
2x² + 7x - 15 = 0
Answer:
2x² + 7x - 15 = 0
A bag holds 5.8lb of corn. How many pounds do 2.5 bags hold
ANSWER:
14.5 pounds
STEP-BY-STEP EXPLANATION:
We know the capacity of each bag, therefore, we can calculate the capacity of 2.5 bags, multiplying by the capacity of one, like this:
[tex]\begin{gathered} c=5.8\cdot2.5 \\ \\ c=14.5\text{ lb} \end{gathered}[/tex]Which means 2.5 bags contain a total of 14.5 lbs.
A builder is buying boxes of nails. She has $187 to spend and each box of nails costs $4. How many boxes of nails can the builder buy?42503746
To find How many boxes of nails can the builder buy divide the total she has into the cost of each box:
Then, she can buy 46 boxes of nailsDr. Walton is studying a bacterial colony with a population of 77,000 bacteria. The colony is growing 15% per hour. How many bacteria will the colony contain in 3 hours?
The colony will contain 117,107 bacteria in 3 hours
Here, we start by writing an exponential function that can represent the question
We have this as;
[tex]N=I(1+r)^t[/tex]N is the number of bacteria at a particular time t
I is the initial number of bacteria which is 77,000
r is the growth rate which is 15% = 15/100 = 0.15
t is the time in hours = 3
Substituting these values, we have it that;
[tex]\begin{gathered} N=77,000(1+0.15)^3 \\ N=77,000(1.15)^3 \\ N\text{ = 117,107} \end{gathered}[/tex]This answer is given to the nearest whole number
is this a positive, negative or no correlation? please help
Answer:
Positive correlation!
Step-by-step explanation:
The lines represented by the equations y = 1/2x-8 and 2y+4x=10
The first equation is in slope-intercept form but the second equation is not. Therefore, our first step is to bring 2y+4x=10 into slope-intercept form.
Subtracting 4x from both sides gives
[tex]2y=10-4x[/tex]finally, dividing both sides by 2 gives
[tex]y=-2x+5[/tex]Now, that we have the equation in slope-intercept form, let us compare their slopes to see how they relate to each other.
The lines are perpendicular if the slope of one line is negative of the reciprocal of the other.
Now, -2 is negative of the reciprocal of 1/2. Meaning if you take the reciprocal 1/2, then multiply it by -1 you will end up with -2.
Since the slope of a negative reciprocal of each other, the lines are perpendicular.
Please help me and explain how to find the result
A family consumes 1.2kg of rice a day
If the family have 30ky of rice
Let the number of days be x
The minimum number of days required for the amount of rice remaining not to be more than 6kg can be expressed below as
[tex]30-1.2x\le6[/tex]Solve for x by collecting like terms
[tex]\begin{gathered} 30-1.2x\le6 \\ 30-6\le1.2x \\ 24\le1.2x \\ 1.2x\ge24 \\ \text{Divide both sides by 1.2} \\ \frac{1.2x}{1.2}\ge\frac{24}{1.2} \\ x\ge20\text{ days} \end{gathered}[/tex]Hence, the minimum number of days required for the amount of rice remaining not to be more than 6kg is 20 days