506.78 meters per min
Explanation:distance = 400 m
time = 47.36 seconds
The result is meant to be in meters/min
We need to convert the seconds to minute:
60 seconds = 1 min
47.36 seconds = 47.36/60 = 0.7893
The average rate will be distance divided by time
[tex]\begin{gathered} \text{Average rate =}\frac{400}{0.7893} \\ \text{Average rate =}\frac{400}{0.7893}\text{ = }506.7782 \\ \\ \text{Average rate = }506.78\text{ meters per min (nearest hundredth)} \end{gathered}[/tex]Dr. 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
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
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]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.
Anthropologists use a linear model that relates femur length to height. The model allows an anthropologist todetermine the height of an individual when only a partial skeleton (including the femur) is found in this problem, wefind the model by analyzing the data on femur length and height for the eight males given in the tableFemur length (cm)49.948.646.345.844.343.639.738.9Height (cm)177.5174.6165.6164.7165.3164.6155.8156.71.Which scatterplot best matches the given data?A.B.2.What is the correlation coefficient for this data?
For the scatter plot (part 1), you should have gotten something like this.
Notice that, in general, the greater the femur length is, the taller the person is. Therefore, the relation between those two quantities has the form
[tex]Y=mX+b,m>0[/tex]And, the correlation coefficient is
[tex]r=\frac{\sum ^{\square}_{\square}(x_i-\bar{x})(y_i-\bar{y})}{\sqrt[]{\sum ^{\square}_{\square}(x_i-\bar{x})^2\sum ^{\square}_{\square}(y_i-y)^2}}[/tex]In our case,
[tex]\begin{gathered} \bar{x}=\frac{1}{8}(49.9+48.6+46.3+45.8+44.3+43.6+39.7+38.9)=44.6375 \\ \bar{y}=\frac{1}{8}(177.5+174.6+165.6+164.7+165.3+164.6+155.8+156.7)=165.6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \sum ^{\square}_{}(x_i-\bar{x})(y_i-\bar{y}_{})=197.83 \\ \end{gathered}[/tex]and
[tex]\begin{gathered} \sum ^{\square}_{\square}(x_i-\bar{x})=105.9987 \\ \sum ^{\square}_{\square}(y_i-\bar{y})=399.76 \end{gathered}[/tex]Finally,
[tex]\Rightarrow r=\frac{197.83}{\sqrt[]{(105.9987)(399.76)}}=0.961[/tex]Thus, the correlation coefficient is equal to 0.961
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".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ1
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.
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.
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]
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.
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.
to learn more about quadrilaterals visit:
https://brainly.com/question/13805601
#SPJ9
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
How much sugar is in a 340 gram mixture if you know the mixture is 50%sugar?
We got 340 gram mixture. The 50% of it is sugar, so:
[tex]\frac{50}{100}\cdot340=170[/tex]Then, there are 170g of sugar.
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.
5+3(-2x+1)=16 I need help
Given:
5 + 3(-2x + 1) = 16
Let's solve for x.
• Step 1:
Use distributive property to expand the parenthesis
5 + 3(-2x) + 3(1) = 16
5 - 6x + 3 = 16
• Step 2:
Combine like terms
-6x + 3 + 5 = 16
-6x + 8 = 16
• Step 3:
Subtract 8 from both sides
-6x + 8 - 8 = 16 - 8
-6x = 8
• Step 4:
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{8}{-6} \\ \\ x=-\frac{4}{3} \end{gathered}[/tex]ANSWER:
[tex]-\frac{4}{3}[/tex]•
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.
A pizza place offers ten different toppings. A special is a pizza with any three different toppings. How many different types of specials are offered?
As given by the question
There are given that the total of 10 different topping
Now,
According to the question:
There is also talk about 3 different pizzas.
So,
The three different toppings from the 10 different toppings:
[tex]10C_3=\frac{10!}{3!(10-3)!}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10!}{3!(10-3)!} \\ 10C_3=\frac{10!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8\times7!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8}{3\times2\times1} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10\times9\times8}{3\times2\times1} \\ 10C_3=10\times3\times4 \\ 10C_3=120 \end{gathered}[/tex]Hence, 120 different pizzas are possible.
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.
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]Find the value of the ratio using the term sequence 5, 15, 45 , 135, ...
To find the ratio, we just have to divide the second term by the first term.
[tex]\frac{15}{5}=3[/tex]Therefore, the ratio of the sequence is 3.Notice that the given sequence is geometrical because we have to multiply each term with 3 to get each new term.
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]Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=8 cm
pi=3.14
substitute the given values in the formula
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot8^3 \\ V=2,143.6\text{ cm\textasciicircum{}3} \end{gathered}[/tex]answer is
2,143.6 cubic centimeterswhat 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
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
QThe image of point A (3, 4) under translation Tis A' (-1,6). What is the translation rule? worth 50 points guy's can someone please give me an answer really quick please!!!
Here, we want to find the translation rule
Given the lines below, create a line that is parallel, one that is perpendicular, and one that is neither. Y = -6Parallel: Perpendicular: Neither:
Given:
[tex]y=-6[/tex]The slope of the given line is zero.
a) parallel line: Parallel lines have the same slope. Any line whose slope is x=zero will be parallel to line y=-6.
So, one equation can be,
[tex]y=-2[/tex]2) Perpendicular line
Clearly the line y=-6 is the horizontal line having a slope of 0.
So, the line perpendicular to this line will be a verticle line with an undefined slope.
And its equation is of the form x = a.
The equation can be,
[tex]x=2[/tex]c) The lines which are neither parallel nor perpendicular will be just the intersecting lines.
The equation can be,
[tex]y=x+1[/tex]Use Pascal's Triangle to expand the binomial. (d-3)^6
Using pascal triangle
(d-3)^6
Expoenent 6 has a coeffient of;
1 6 15 20 15 6 1
Hence;
[tex]d^6-6(d)^5(3)+15(d)^4(3)^2-20(d)^3(3)^3+15(d)^2(3)^4-6(d)(3)^5+3^6[/tex]Two things to note here is that;
-There is a minus sign in-between the numbers in the bracket, hence we alternate the sign starting with positive
-secondly as the power of the first variable decreases the power of the second digit increases
We can further simplify;
[tex]d^{6\text{ }}-6d^5(3)+15(d)^4(9)^{}-20d^3(27)+15d^2(81)-6d(243)+729[/tex]We will still simplify to give:
[tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d\text{ + 729}[/tex]Answer:
The Binomial Theorem Quick Check:
1. [tex]d^6-18d^5+135d^4-540d^3+1215d^2-1458d+729[/tex]
2. [tex]s^5+15s^4v+90s^3v^2+270s^2v^3+405sv^4+243v^5[/tex]
3. [tex]-64b^3[/tex]
100% 3/3
You're Welcome! A brainliest would help me alot. ‿
is this a positive, negative or no correlation? please help
Answer:
Positive correlation!
Step-by-step explanation:
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]what 3 1/4 - 1 3/8 equal?
Answer : 1 7/8
Given that: 3 1/4 - 1 3/8
Step 1: Convert the mixed fraction into an improper fraction
3 1/4 = (4 x 3) + 1 / 4
3 1/4 = 12 + 1 / 4
3 1/4 = 13/4
1 3/8 = (8 x 1) + 3 / 8
1 3/8 = 8 + 3 / 8
1 3/8 = 11/8
13/4 - 11/8
The common denominator is 8
2 x 13 - 11 x 1 / 8
26 - 11 / 8
15/8
1 7/8
Therefore, the answer is 1 7/8