In order to calculate the cost for 3 pounds of acorn squash, we can write the following rule of three:
[tex]\begin{gathered} \text{weight}\to\text{cost} \\ 4\text{ pounds}\to6.36 \\ 3\text{ pounds}\to x \end{gathered}[/tex]Then, we can write the following equation and solve it for x:
[tex]\begin{gathered} \frac{4}{3}=\frac{6.36}{x} \\ 4\cdot x=3\cdot6.36 \\ 4x=19.08 \\ x=\frac{19.08}{4} \\ x=4.77 \end{gathered}[/tex]Therefore the cost of 3 pounds is $4.77.
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.2, 10, 15, 4. 14. 7. 14, 8, 2, 10The range is(Simplify your answer.)The population mean is(Simplify your answer. Round to the nearest tenth as needed.)The population variance is I(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is(Simplify your answer. Round to the nearest tenth as needed)Enter your answer in each of the answer boxes.
The numbers of regular-season wins for 10 football teams in a given season are given below
[tex]2,10,15,4,14,7,14,8,2,10[/tex]We are asked to find the range, mean, variance, and standard deviation of the population data set.
Range:
The range is the difference between the maximum value and the minimum value in a data set.
From the given data set,
Maximum value = 15
Minimum value = 2
[tex]\begin{gathered} \text{Range}=\text{maximum}-\text{minimum} \\ \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}[/tex]Therefore, the range is 13
Mean:
The population mean is given by
[tex]\mu=\frac{\sum^{}_{}X}{N}[/tex]Where X is the terms in the data set and N is the number of terms in the data set.
[tex]\begin{gathered} \mu=\frac{2+10+15+4+14+7+14+8+2+10}{10} \\ \mu=\frac{86}{10} \\ \mu=8.6 \end{gathered}[/tex]Therefore, the population mean is 8.6
Variance:
The population variance is given by
[tex]\sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N}[/tex]Where X is the terms in the data set, μ is the mean, and N is the number of terms in the data set.
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N} \\ \sigma^2=\frac{(2-8.6)^2+(10-8.6)^2+(15-8.6)^2+(4-8.6)^2+(14-8.6)^2+(7-8.6)^2+(14-8.6)^2+(8-8.6)^2++(2-8.6)^2++(10-8.6)^2}{10} \\ \sigma^2=\frac{214.4}{10} \\ \sigma^2=21.4 \end{gathered}[/tex]Therefore, the population variance is 21.4
Standard deviation:
The population standard deviation is given by
[tex]\begin{gathered} \sigma^{}=\sqrt[]{\frac{\sum^{}_{}(X-\mu)^2}{N}} \\ \sigma=\sqrt[]{\sigma^2} \end{gathered}[/tex]Since we have already find the population variance, we can simply find take the square root of variance.
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{21.4} \\ \sigma=4.6 \end{gathered}[/tex]Therefore, the population standard deviation is 4.6
How come my answer is wrong? It says it’s equal to the correct answer but it’s not the right answer.
What is the sum of the exterior angles of a polygon with 30 sides a) 180°b) 30°c) 90°d) 360°
Note that:
The sum of the exterior angles of a polygon does not depend on the number of sides of the polygon
The sum of the exterior angles of a polygon is 360°
Therefore, the correct option is 360°
From the diagram below, if side AB is 36 cm., side DE would be ______.
Given
AB = 36 cm
Find
Side DE
Explanation
here we use mid segment theorem ,
this theorem states that the mid segment connecting the mid points of two sides of a triangle is parallel to the third side of the triangle and the length of the midsegment is half the length of the third side.
so , DE = 1/2 AC
DE = 36/2 = 18 cm
final Answer
therefore , the correct option is c
A tornado siren begins blaring from the center of town 9.5 seconds after a tornado was spotted. The siren is located 490 meters north of a school. If the siren’s sound wave travels at a constant velocity of 350 meters per second south, how long will it take the sound wave to travel from the siren to the school?
The relationship between distance, time and velocity is:
[tex]v=\frac{d}{t}[/tex]The question ask us for the time, we can solve for t:
[tex]v=\frac{d}{t}\Rightarrow t=\frac{d}{v}[/tex]To find the time that it will take the sound wave travelling at 350 m/s to reach the school at 490m is the distance divided the velocity:
[tex]\begin{gathered} t=\frac{490m}{350\frac{m}{s}} \\ \end{gathered}[/tex][tex]t=1.4s[/tex]The answer is 1.4s
Suppose that $2000 is invested at a rate of 3.9%, compounded monthly. Assuming that no withdrawals are made, find the total amount after six years.Round your answer to the nearest cent.
Compound interest formula:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ A\colon\text{Amount} \\ P\colon\text{ Principal} \\ r\colon\text{ interest rate (in decimals)} \\ n\colon\text{ number of times interest is compounded in a year} \\ t\colon\text{ time (in years} \end{gathered}[/tex]Given data:
P= $2,000
r= 3,9% =0.039
n=monthly= 12
t= 6 years
[tex]\begin{gathered} A=2000(1+\frac{0.039}{12})^{12(6)} \\ \\ A=2000(1.00325)^{72} \\ \\ A\approx2526.33 \end{gathered}[/tex]Then, the total amount after six years is $
Okay so I’m doing this assignment and got stuck ont his question can someone help me out please
ANSWER
[tex]B.\text{ }\frac{256}{3}[/tex]EXPLANATION
We want to find the value of the function for F(4):
[tex]F(x)=\frac{1}{3}*4^x[/tex]To do this, substitute the value of x for 4 in the function and simplify:
[tex]\begin{gathered} F(4)=\frac{1}{3}*4^4 \\ F(4)=\frac{1}{3}*256 \\ F(4)=\frac{256}{3} \end{gathered}[/tex]Therefore, the answer is option B.
!!PLEASE ANSWER FAST PLEASE!! Given f(x)=(1/4)(5-x)² what is the value of f(11)
Answer:
f(11) = 9
Explanation:
The equation for f(x) is:
[tex]f(x)=\frac{1}{4}(5-x)^2[/tex]To know the value of f(11), we need to replace x by 11 and solve, so:
[tex]\begin{gathered} f(11)=\frac{1}{4}(5-11)^2 \\ f(11)=\frac{1}{4}(-6)^2 \\ f(11)=\frac{1}{4}(36) \\ f(11)=9 \end{gathered}[/tex]Therefore, the value of f(11) is 9.
What are the solutions to the equation (x-3)(x+5)=-15
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
What is the equation?
A mathematical statement that shows that two mathematical expressions are equal.
Here given expression is
[tex](x-3)(x+5)=-15\\\\x^2+5x-3x-15=-15\\\\x^2+5x-3x=0\\\\x^2+2x=0\\\\x(x+2)=0\\\\x=0,-2[/tex]
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
To know more about the equation
https://brainly.com/question/12788590
#SPJ2
estimate 2,829 divided by 33=?
Answer: 100
Step-by-step explanation:
Calculate it and 85.7272727273 is closer to 100 so its 100
The fraction models below represent two fractions of the same whole: How much of the8음을16
So 4/5 times 5/8 is 1/2.
2x^3+ 15^2+ 27x + 5= x^2+ 5x + 12x + 5
To determine if the equation is true we multiply the expression on the right side by the denominator on the left; if the result is the numerator on the left then the equation is true:
[tex]\begin{gathered} (2x+5)(x^2+5x+1)=2x^3+10x^2+2x+5x^2+25x+5 \\ =2x^3+15x^2+27x+5 \end{gathered}[/tex]Since the result is the numerator on the left side we conclude that the equation is true.
Question60 is 40% of what number?
let the required number be x then
[tex]\begin{gathered} \frac{60}{x}\times100=40 \\ x=\frac{60}{40}\times100 \\ x=150 \end{gathered}[/tex]So 60 is 40% of 150.
Nathan loved learning about earthquakes in science class. He told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute. What would be the most appropriate unit for Nathan to use instead of centimeters per minute?
The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.
What is an earthquake?An earthquake simply means a rapid motion of the solid layer of the Earth.
In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.
Since the year is being discussed, the unit should be based on the year.
Learn more about earthquake on:
brainly.com/question/248561
#SPJ1
Shawn pays a rate of 35.55 mills in property tax on a home with an assessed value of $63,500. What is his property tax?
Answer:
$2257.425
Explanation:
A rate of 35.55 mills means that they have to pay 35.55 per each $1000 in the assessed value. If the assessed value is 63,500, we can calculate his property tax as
[tex]63,500\times\frac{35.55}{1000}=2257.425[/tex]Therefore, the answer is $2257.425
Need help !! Geometry unit 3 parallel and perpendicular lines
ANSWER;
Converse; Exterior alternate angles are equal
[tex]x\text{ = 3}[/tex]EXPLANATION;
Here, we want to get the value of x given that the lines l and m are parallel
From the diagram given, we can see that;
[tex]15x\text{ +29 = 26x-4}[/tex]The reason for this is that they are a pair of exterior alternate angles
Mathematically, exterior alternate angles are equal
From here, we can proceed to solve for the value of x;
[tex]\begin{gathered} 26x-15x\text{ = 29+4} \\ 11x=33 \\ x\text{ = }\frac{33}{11} \\ x\text{ = 3} \end{gathered}[/tex]What’s 1/5 + 1/2 ? Pls help me
We need to calculate 1/5 + 1/2:
H = 1/5 + 1/2
Then: H = 7/10
the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
Let
L ------> the lenght
W ----> the width
we know that
the area of rectangle is
A=L*W
A=63 yd2
63=L*W -------> equation 1
and
L=2W+11 ------> equation 2
substitute equation 2 in equation 1
63=(2W+11)*w
2W^2+11w-63=0
solve the quadratic equation using the formula
a=2
b=11
c=-63
substitute
[tex]w=\frac{-11\pm\sqrt[]{11^2-4(2)(-63)}}{2(2)}[/tex][tex]\begin{gathered} w=\frac{-11\pm\sqrt[]{625}}{4} \\ \\ w=\frac{-11\pm25}{4} \\ \end{gathered}[/tex]the solutions for W are
w=3.5 and w=-9 (is not a solution, because is negative)
so
Find the value of L
L=2W+11 -------> L=2(3.5)+11
L=18
therefore
the dimensions are
Length is 18 yardsWidth is 3.5 yardsGraph the following equation:(y + 4) = 2(x - 2)Step 1 of 3: Find a point on the line and the slope of the line.
Given:
The equation of line is,
[tex]y+4=2(x-2)[/tex]Find the slope of equation,
[tex]\begin{gathered} y+4=2(x-2) \\ y+4=2x-4 \\ y=2x-8 \\ \text{slope= 2} \end{gathered}[/tex]Find the points on line,
[tex]\begin{gathered} \text{For x=0,} \\ y=2x-8 \\ y=-8 \\ (x,y)=(0,-8) \\ \text{for x=4,} \\ y=2x-8 \\ y=2(4)-8 \\ y=0 \\ (x,y)=(4,0) \\ \text{For x=2} \\ y=2x-8 \\ y=2(2)-8=-4 \\ (x,y)=(2,-4) \\ \text{For }x=5 \\ y=2x-8 \\ y=2(5)-8=2 \\ (x,y)=(5,2) \end{gathered}[/tex]The graph of equation of line is,
A box contains six red pens, four blue pens, eight green pens, and some black pens. Leslie picks a pen and returns it to the box each time. The outcomes are recorded in the table.a. what is the experimental probability of drawing a green pen?b. if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box
given the follwing parameters,
number of times a Red Pen is picked is 8
numbr o f times the Blue Pen is picked is 5
Number of times the Green Pen is picked is 14
Number of times the Black Pen is picked is 3
so,
(a) to get the experimental probability of drawing a Green Pen is,
P = favoured results/all obtained
then,
14/(8+5+14+3)
= 14/30 that is a
(
Simplify each expression.26. -2 · 11ly27. -5s(-4t)28. 3(-p)(-2q)29. -j(11k)30. 7x(-2y)
We need to multiply each term in the expression and take into account the rules for signs.
The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)
We can find W and L using the sine and the cosine functions:
[tex]\begin{gathered} \sin (30)=\frac{W}{14} \\ so\colon \\ W=14\cdot\sin (30) \\ --------- \\ \cos (30)=\frac{L}{14} \\ so\colon \\ L=14\cdot\cos (30) \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} A=L\cdot W \\ A=14\cdot\cos (30)\cdot14\cdot\sin (30) \\ A=49\sqrt[]{3} \\ A\approx84.87cm^2 \end{gathered}[/tex]Answer:
84.87 cm²
Point L is on line segment KM. Given KL = 15 and LM = 3, determine the
length KM.
Answer: KM = 18
Step-by-step explanation:
K---------------L---M
15 + 3 = 18
Factoring the polynomial 12g + 20h
3. Which of the following points would produce a negative slope? (A) (B) (C) (D) (-1,2) and (4,2) (-2,-2) and (0,4) (1,3) and (-1,4) (2,4) and (-2,-1)
The sequation to calculate the slope is,
[tex]m=\frac{y2-y1}{x2-x1}[/tex]The solpe of line joining (-1,2) and (4,2) is,
[tex]\begin{gathered} m=\frac{2-2}{4+1} \\ m=0 \end{gathered}[/tex]The slope of the line joining (-2,-2) and (0,4) is,
[tex]\begin{gathered} m=\frac{4+2}{0+2} \\ m=3 \end{gathered}[/tex]The slope of the line joining (1,3) and (-1,4) is,
[tex]\begin{gathered} m=\frac{4-3}{-1-1} \\ m=-\frac{1}{2} \end{gathered}[/tex]Negative slope.
The slope of the line joining (2,4) and (-2,-1) is,
[tex]\begin{gathered} m=\frac{-1-4}{-2-2} \\ m=\frac{5}{4} \end{gathered}[/tex]Positive slope.
How do I solve this and what is the answer
Answer:
Answer is 20 degrees
:)
how to solve 2x^2-3x-1=0
Explanation
[tex]2x^2-3x-1=0[/tex]Step 1
remember the quadratic formula.
if you have the equation
[tex]ax^2+bx+c=0[/tex]the value for x is
[tex]x=\frac{-b^2+\sqrt{b^2}-4ac}{2a}[/tex]Step 2
let
[tex]ax^2+bx+c=2x^2-3x-1[/tex]a=2
b=-3
c=-1
Step 3
replace
[tex]undefined[/tex]A hot air balloon was descending at a rate of 25 feet per minute and was known to be at an altitude of 425 feet above the ground 21 minutes after it began its descenta) determine the slope-intercept form of the equationb) How high was the balloon when it began its descent (0 minutes)c) How many minutes did it take to land?
We can model the problem as a linear equation of the form:
[tex]y=mx+b[/tex]Where:
m = Slope (Rate of change)
b = y-intercept (Initial value)
a)
Since it is descending at a rate of 25ft per minute, the slope is:
[tex]m=-25[/tex]So, the equation is:
[tex]y=-25x+b[/tex]b) We know that the ballon was 425ft above the ground 21 minutes after it began its descent, so:
[tex]\begin{gathered} y=425,x=21 \\ so\colon \\ 425=-25(21)+b \\ 425=-525+b \\ b=950 \end{gathered}[/tex]Therefore, the balloon was 950ft when it began its descent, so, we can conclude that the y-intercept is 950, now the equation is complete
[tex]y=-25x+950[/tex]c) We need to know for which value of x, y is equal to 0, so:
[tex]\begin{gathered} y=0 \\ 0=-25x+950 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 25x=950 \\ x=\frac{950}{25} \\ x=38 \end{gathered}[/tex]The balloon will land after 38 minutes
Teresa surveyed 100 students about whether they like pop music or country music. Outof the 100 students surveyed, 42 like only pop, 34 like only country, 15 like both popandcountry, and 9 do not like either pop or country. Complete the two-way frequency table.
SOLUTION
Write out the given information
[tex]\begin{gathered} \text{Total number of student surveyed=100} \\ \text{like pop only=42} \\ \text{like country only=34} \end{gathered}[/tex][tex]\begin{gathered} \text{like both pop and country=15} \\ Do\text{ not like any =9} \end{gathered}[/tex]Construct the two- way frequency table
For questions 5&6 find F -1(x), the inverse of F(x)
To find the inverse function, we can follow the next steps:
First Function1. Replace x with y as follows:
[tex]y=3x+7\Rightarrow x=3y+7[/tex]2. Solve the resulting equation for y. Subtract 7 from both sides of the equation:
[tex]x-7=3y+7-7\Rightarrow x-7=3y[/tex]3. Divide both sides of the equation by 3:
[tex]\frac{(x-7)}{3}=\frac{3}{3}y\Rightarrow y=\frac{(x-7)}{3}=\frac{1}{3}(x-7)=\frac{x}{3}-\frac{7}{3}[/tex]Second FunctionWe need to repeat the process to obtain the inverse of this function:
1. Replace x with y:
[tex]y=8x\Rightarrow x=8y[/tex]2. Solve for y. Divide both sides by 8:
[tex]\frac{x}{8}=\frac{8}{8}y\Rightarrow y=\frac{x}{8}[/tex]In summary, we have that the inverse functions are:
For function
[tex]y=3x+7[/tex]The inverse function is:
[tex]y=F^{-1}^{}(x)=\frac{(x-7)}{3}[/tex]And, for the function
[tex]y=8x[/tex]The inverse function is:
[tex]y=f^{-1}(x)=\frac{1}{8}x[/tex]