Mean = sum of the terms/number of terms
Replacing with data:
Mean = (37*0 + 51*30 + 17*45 + 20*60 + 19*75 + 11*90 + 50*120 + 45*240)/250
= 90.84 minutes
how do you solve 15w-4=41
In order to solve this equation for w, we can do the following steps:
[tex]\begin{gathered} 15w-4=41 \\ 1.\text{ Add +4 to both sides of the equation:} \\ 15w-4+4=41+4 \\ 15w=45 \\ 2.\text{ Divide both sides of the equation by 15:} \\ \frac{15w}{15}=\frac{45}{15} \\ w=3 \end{gathered}[/tex]So we have that the value of w is 3.
Hello! Use interval notation to indicate all real numbers between −3 and 5 , including −3 but not including 5.
Given:
The real numbers given as -3 and 5
Required:
We need to indicate all real numbers between −3 and 5 , including −3 but not including 5
Explanation:
Use [ to include the number and use ) to not include the number
So here we want to include -3 so use [ with -3 and we do not want to incluse 5 so use ) with 5
There is a rule that we need to start with small number and here the small number is -3 among -3 and 5
FInal answer:
[-3,5)
What is the value of the algebraic expression if x = 1/2, y = -1, and z = 2?Here is the algebraic expression: 6x(y to second power z)
The value of the algebraic expression if x = 1/2, y = -1, and z = 2 is 6.
The given expression is [tex]6xy^{2}z[/tex] and we need to evaluate its value when x = 1/2, y = -1, and z = 2
Simply assign the values of each variable to the variables in the algebraic expression and evaluate the result to get the value of the expression. What we do is:
[tex]6xy^{2}z\\\\=6 * \frac{1}{2}*(-1)^{2} *2 \\\\=6 * \frac{1}{2}*1 *2\\\\=6[/tex]
The algebraic expression's value would be 6, then. In an algebraic expression, the variables are denoted by letters, in this case x, y, and z; the coefficients are denoted by numbers, such as 6, and the exponents are, in this case, 2, as in the expression above. Expressions frequently include several terms made up of those components.
To read more about algebraic expressions, visit https://brainly.com/question/953809
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Dominic has a bag of candy full of 1 strawberry chew and 19 cherrychews that he eats one at a time. Which word or phrase describes theprobability that he reaches in without looking and pulls out a lemonchew?A.certainB.unlikelyC.likelyD.impossible
D.impossible
there is no Lemon chew, only strawberry chew and cherry chews
a card is drawn at random from a standard deck. Determine whether the events are mutually exclusive or not mutually exclusive. Then find each probability. P(jack or 4)
Mutually exclusive events:
Two events are mutually exclusive if they cannot occur at the same time.
There are 52 cards in a deck of cards.
n(s)=52.
Let A be event of getting jack.
n(A)=4.
So, Probability of getting jack is,
Let B be event of getting 4
n(B)=4.
So, Probability of getting 4 is,
[tex]\begin{gathered} P(B)=\frac{n(B)}{n(s)} \\ =\frac{4}{52} \end{gathered}[/tex]These two events do not occur at same time.
Therefore the events are mutually exclusive.
[tex]P(A\cap B)=0[/tex]To find the probability of getting jack or 4
[tex]P(\text{A }\cup\text{B)}=P(A)+P(B)-P(A\cap B)[/tex]hence,
[tex]\begin{gathered} P(\text{A }\cup\text{B)}=\frac{4}{52}+\frac{4}{52}-0 \\ =\frac{8}{52} \\ =\frac{2}{13} \end{gathered}[/tex]The probability of getting jack or 4 is,
[tex]\frac{2}{13}[/tex]pls help me with this one & the ones after it !!!
In the given triangle,
line IF is parallel to line HG,
By the basic proportionality theorem,
[tex]\begin{gathered} \frac{JI}{IH}=\frac{FJ}{FG} \\ \frac{25}{20}=\frac{FJ}{28} \\ \frac{25\cdot28}{20}=FJ \\ FJ=35 \end{gathered}[/tex]Answer: FJ=35
convert 15.7cm of the circumference to inches
Answer: We have to convert 15.7cm into inches, the steps for the conversion are as follows:
[tex]\begin{gathered} 1in=2.54cm\rightarrow\frac{1\imaginaryI n}{2.54cm}=1 \\ \\ \frac{15.7cm}{1}\times\frac{1in}{2.54cm}=\frac{15.7}{2.54}in \\ \\ =6.18in \end{gathered}[/tex]Therefore the answer is 6.18in.
Solve using substitution. 6x + y = 5 -8x - 5y = 19 how do I do this
The given system of equations is
[tex]\begin{gathered} 6x+y=5 \\ -8x-5y=19 \end{gathered}[/tex]To solve the system, first, let's multiply the first equation by 5.
[tex]\begin{gathered} 30x+5y=25 \\ -8x-5y=19 \end{gathered}[/tex]Then, we combine the equations
[tex]\begin{gathered} 30x-8x+5y-5y=25+19 \\ 22x=44 \\ x=\frac{44}{22} \\ x=2 \end{gathered}[/tex]Now, we find y
[tex]\begin{gathered} 6x+y=5 \\ 6\cdot2+y=5 \\ 8+y=5 \\ y=5-8 \\ y=-3 \end{gathered}[/tex]Hence, the solution is (2,-3).a rectangle is drawn so the width is 71 inches longer than the height if the rectangles diagonal measurement is 85 inches find the heightround to 1 decimal place______inches
Let's first conceptualize the given details by drawing a rectangle with the given details being reflected.
Where,
x = Height of the rectangle
x + 71 = The ratio of the width of the rectangle with respect to the height.
Cutting the rectangle in half along the diagonal line makes a right triangle,
Thus, we can use the Pythagorean Theorem to be able to determine the height of the rectangle. We get,
[tex]\text{ a}^2+b^2=c^2\text{ }\rightarrow(x+71)^2+(x)^2=(81)^2_{}[/tex][tex]\text{ x}^2+142x+5041+x^2\text{ = 6561}[/tex][tex]\text{ 2x}^2\text{ + 142x + 5041 - 6561 = 0}[/tex][tex](\frac{1}{2})\text{ (2x}^2\text{ + 142x - }1520)\text{ = 0}[/tex][tex]\text{ x}^2\text{ + 71x - 760 = 0}[/tex][tex]\text{ (x +}\frac{71+\sqrt[]{8081}}{2})(x\text{ + }\frac{71\text{ - }\sqrt[]{8081}}{2})=\text{ 0}[/tex]There are two possible height of the rectangle,
[tex]x_1\text{ = }\frac{-71-\sqrt[]{8081}}{2}\text{ = -80.45 in.}[/tex][tex]\text{ x}_2\text{ = }\frac{-71\text{ + }\sqrt[]{8081}}{2\text{ }}=9.45\text{ in.}[/tex]9.45 = 9.5 in. is the most probable height of the rectangle because a dimension must never be negative, thus, let's adopt 9.5 in. as the height.
The width must be = x + 71 = 9.5 + 71 = 80.5 in.
I need help I’ve been having trouble with this chapter for about a week
Given:
[tex]3x^2+20x+33[/tex]Find-:
Factorization of the equation.
Sol:
A simple method of factorization is to multiply in first and last order then break it down into parts to make the middle number then.
[tex]\begin{gathered} =3\times33 \\ =99 \end{gathered}[/tex]
The factor of 99 is:
So take factor :
[tex]\begin{gathered} 11\text{ and \lparen3}\times3) \\ \\ 11\text{ and 9} \end{gathered}[/tex]Factorization of the equation is:
[tex]\begin{gathered} =3x^2+20x+33 \\ \\ =3x^2+11x+9x+33 \end{gathered}[/tex]6 in. SA = 2ten2 + 2trh (Use 3.14 for a.) Find the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches. square inches 8 in. Do NOT round your answer.
207.24 in²
1) Gathering the data
height: 8"
Base Diameter: 6" then a Radius: 3 for D=2R
2) Let's find the Surface Area from this Cylinder by plugging into that the given data:
[tex]\begin{gathered} SA=2\pi\cdot r^2+2\pi rh \\ S_A=2(3.14)\cdot(3)^2+2\cdot3.14\cdot3\cdot8 \\ S_A=207.24in^2 \end{gathered}[/tex]3) Hence, the answer is 207.24 in²
What is 73 / 6? I need a whole number, not 12.1666667 with a remainder if there is one!
/= divided by
Answer:
12
Step-by-step explanation:
12.1666667 rounded:
12.1666667 You rounded to the nearest one's place. The 2 in the ones place rounds down to 2 or stays the same because the digit to the right in the tenth place is 1.
12 When the digit to the right is less than 5 we round toward 0.
12.1666667 was rounded down toward zero to 12
Hi I really do need help with this question. You don’t have to show work but it says we have to explain our answer.
The Solution:
Pattern A: start with 1 and add 3.
[tex]1,\text{ 4, 7, 10, 13}[/tex]Pattern B: Start with 1 and add 4.
[tex]1,\text{ 5, 9, 13, 17}[/tex]Comparing the two patterns, we have that:
Recall:
Median means the middle number.
The median of pattern A is 7 while that of pattern B is 9.
Thus, the median of pattern B is more than the median of pattern A by 2.
I need help NUMBER 181.Find the GCF2.Write the GCF 3.Rewrite expression factor out the GCF4. Write the final factored expression!
Answer:
1. Find the GCF:
16 y | 5
1
2. Write the GCF: 1
3. Rewrite expression factor out the GCF: 16y + 5
4. Write the final factored expression: 16y + 5
Explanation:
The initial expression is:
16y + 5
So, we have two terms: 16y and 5
The factors of these terms are:
16y: 1, 2, 4, 16, y, 2y, 4y, 16y
5: 1, 5
So, the greatest common factor is 1
Then, the expression factor out the GCF is:
[tex]\frac{16y+5}{1}=16y+5[/tex]Therefore, the final factored expression is:
1*(16y + 5) = 16y + 5
Ryan is 6 feet tall. At a certain time of day, he casts a shadow that is 12 feet long. At the same time, a tree casts ashadow that is 28 feet long. What is the height of the tree?
First, notice that Ryan and its shadow form a right triangle with the following measures:
and with the tree, we have the following triangle:
since both triangles are similar, we can write the following proportions:
[tex]\frac{x}{6}=\frac{28}{12}[/tex]where 'x' represent the height of the tree. Solving for 'x', we get:
[tex]\begin{gathered} \frac{x}{6}=\frac{28}{12} \\ \Rightarrow x=\frac{28}{12}\cdot6=\frac{28\cdot6}{12}=\frac{168}{12}=14 \\ x=14ft \end{gathered}[/tex]therefore, the height of the tree is 14 feet
Graph f(x)=log1/2 (x)
The coordinate are (0.8,0)
Answer:
Step-by-step explanation:
Decide if each fraction expressed as a decimal terminates or repeats.
A. 12/11
B. 5/8
C. -19/20
D. 2/3/6/5
Answer:
A. repeat
B. terminates
C. terminates
D. terminates
Step by step explanation:
to turn the fractions into decimals you have to divide the top by bottom
12÷11=1.0909090909
5÷8=0.625
-19÷20=-0.95
2÷3=0.6666666667 6÷5=1.2 ÷0.6666666667 =0.5555555556
only 1 repeats itself multiple times which means thats the only one the repeats and the rest terminate because they end
Jameson downloaded one digital song for $1.25, two digital songs for $2.50, and 5 digital songs for $6.25. solve the equation to find the cost to download 20 digital songs
The cost of downloading 20 digital songs = 20 x 1.25
how can we determine key words to find what kind of sign to use
The problem says there are:
2 neighbors with birds
10 neighbors with cats
8 neighbors with dogs.
As each neighbor owns only one pet, the total number of neighbors is then:
2+10+8=20
The percentage of the neighbors that own dogs is the number of neighbors with dogs, divided by the total number of neighbors, then:
[tex]\frac{8}{20}\times100=\frac{4}{10}\times100\text{ \%=0.4x100\%=40\%}[/tex]Then the 40% of the neighborhood pet owners have dogs.
You want to invest $1000 in an account and plan to leave it there for 12 years. There are three options for investing your money.Account A pays 14% interest per year, compounded annually.Account B pays 13.6% interest per year, compounded monthly.Account C pays 13% interest per year, compounded daily.
Round 58,300 to the nearest ten thousand 
ok
Rounding to the nearest 10000 the result is
60,000
Answer:
60,000
Step-by-step explanation:
The 5 is in the ten-thousands place.
Make all digits right of the 5 into a zero.
You get 50,000.
Since 8 (in the thousands place) is greater than 5, the ten-thousands place goes uo 1 to 6.
Answer: 60,000
If you randomly select a card from a well-shuffled standard deck of 52 cards, determine the probabilitythat the card you select is not a 6.a) Write your answer as a reduced fraction.b) Write your answer as a decimal, rounded to the nearest thousandth.c) Write your answer as a percent. Round to the nearest tenth of a percent as needed.
Answer:
The probability that a card selected at random is not a 6 is:
a. 12/13
b. 0.923
c. 92.3
Explanation:
There are 4 6's in a well-shuffled deck of cards.
The probability that a card selected at random is not a 6 is:
1 - (The probability that it is a 6)
= 1 - 4/52
= 12/13
b. As a decimal, we have 0.923
c. As a percentage, we have 92.3%
Using the image below. Write the equation of the line fully simplified slope-intercept form. NO SPACES BETWEEN TERMS * just letting you know the answer is not y=-5x+2 or y=6x+2
The slope-intercept form is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]From the given graph, the line passes through points (1, -4) and (0, 2)
Let (x1, y1) = (1, -4) and (x2, y2) = (0, 2)
[tex]\begin{gathered} m=\frac{2-(-4)}{0-1} \\ m=\frac{2+4}{-1} \\ m=\frac{6}{-1} \\ m=-6 \end{gathered}[/tex]Substitute the value of m in the form of the equation
[tex]y=-6x+b[/tex]Since the line intersects the y-axis at point (0, 2)
Then the y-intercept is 2
Then b = 2
The equation of the line is
[tex]y=-6x+2[/tex]Write the coordinates of the vertices after a reflection over the x-axis. 1072
The reflection about x-axis results in same x coodinate with oppositive of y coordinate. It can be expressed as,
[tex](x,y)\rightarrow(x,-y)[/tex]Determine the coordinates of the vertices after reflection over the x-axis.
[tex]Q(6,-8)\rightarrow Q^{\prime}(6,8)[/tex][tex]R(7,-8)\rightarrow R^{\prime}(7,8)[/tex][tex]S(7,-5)\rightarrow Q^{\prime}(7,5)[/tex][tex]T(6,-5)\rightarrow T^{\prime}(6,5)[/tex]Please help answer questions one through fiveApply the transformation (a to c) on ABC to get an image
Answer:
d) area of the pre- image will be less than the new image
e) it is
Explanation:
Given:
Triangle ABC on a coordinate plane
To find:
the transformation on the original image
We need to state the vertices of the triangle ABC:
A = (-1, 2)
B = (-2, 1)
C = (0, 0)
a) dilation by a scale factor of 4
[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen4x, 4y\rparen} \\ A=\text{ \lparen4\lparen-1\rparen, 4\lparen2\rparen\rparen = \lparen-4, 8\rparen} \\ B\text{ = \lparen4\lparen-2\rparen, 4\lparen1\rparen\rparen = \lparen-8, 4\rparen} \\ C=\text{ \lparen4\lparen0\rparen, 4\lparen0\rparen\rparen = \lparen0, 0\rparen} \end{gathered}[/tex]b) reflect over the x axis:
[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow\text{ \lparen x, -y\rparen} \\ We\text{ will negate all the y values of the vertices above while keeping x coordinate constant} \\ A\text{ = \lparen-4, -8\rparen} \\ B\text{ = \lparen-8, -4\rparen} \\ C=\text{ \lparen0, -0\rparen = \lparen0, 0\rparen} \end{gathered}[/tex]c) dilate by 1/2
[tex]\begin{gathered} (x,\text{ y\rparen }\rightarrow(\frac{1}{2}x,\text{ }\frac{1}{2}y) \\ We\text{ will multiply the coordinates above by 1/2 in both the x and y coordinates} \\ A^{\prime}\text{ = \lparen}\frac{1}{2}(-4),\text{ }\frac{1}{2}(-8))\text{ = \lparen-2, -4\rparen} \\ B^{\prime}\text{ = \lparen}\frac{1}{2}(-8),\text{ }\frac{1}{2}(-4))\text{ = \lparen-4, -2\rparen} \\ C^{\prime}\text{ = \lparen}\frac{1}{2}(0),\text{ }\frac{1}{2}(0))\text{ = \lparen0, 0\rparen} \\ \\ Image\text{ of ABC: A' \lparen-2, -4\rparen, B' \lparen-4, -2\rparen and C' = \lparen0, 0\rparen} \end{gathered}[/tex]d) To determine if the area of the pre-image is greater or less than, we will plot the coordinates of both triangles:
Since the triangle of the Image is greater than the triangle of the pre-image (original figure), then the area of the pre- image will be less than the new image
e) For two triangles to be congruent, the sides and angles for both triangles will be equal
For two triangles to be similar, the ratio of their corresponding sides will be equal
The image A'B'C' is a scaled triangle of ABC. This mean the sides can't be equal but the ratio fo their corresponding sides will be equal.
Hence, it is simlar
Use the fundamental identities to find the value of trigonometric function. Find csc θ, given that sin 2θ = - — and θ is in quadrant IV. 3
Recall that:
[tex]\csc \theta=\frac{1}{\sin\theta}\text{.}[/tex]If:
[tex]\sin \theta=-\frac{2}{3},[/tex]then:
[tex]\csc \theta=\frac{1}{-\frac{2}{3}}\text{.}[/tex]Simplifying the above result we get:
[tex]\csc \theta=-\frac{3}{2}\text{.}[/tex]Answer:
[tex]\csc \theta=-\frac{3}{2}\text{.}[/tex]Suppose that tan(x)csc(x)=1/f(x).Write f(x) in terms of sin(x) and cos(x).f(x)=
Trigonometry
We are given the equation:
[tex]\tan (x)\csc (x)=\frac{1}{f(x)}[/tex]It's required to write f(x) in terms of the sine and cosine functions.
Taking the reciprocal of both sides of the equation:
[tex]f(x)=\frac{1}{\tan (x)\csc (x)}[/tex]Recall:
[tex]\begin{gathered} \tan (x)=\frac{\sin (x)}{\cos (x)} \\ \text{csc(x)}=\frac{1}{\sin (x)} \end{gathered}[/tex]Substituting:
[tex]f(x)=\frac{1}{\frac{\sin(x)}{\cos(x)}\frac{1}{\sin (x)}}[/tex]Simplifying:
[tex]f(x)=\frac{1}{\frac{1}{\cos(x)}}=\cos (x)[/tex]Thus:
f(x)= cos(x)
Determine the initial investment, PV, for a future value of 6500 dollars if the nominal rate of interest is 5.9 percent compounded quarterly for 12 years? FV = PV(1 + r/n) ^ntPv = ________ (Be sure to give 2 decimal places of accuracy.)
Answer: PV = 3218.69
Explanation:
The formula for calculating compound interest is expressed as
FV = PV(1 + r/n) ^nt
Where
FV is the future value
PV is the initial value
r is the interest rate
n is the number of compounding periods in a year
t is the number of years
From the information given,
FV = 6500
r = 5.9% = 5.9/100 = 0.059
n = 4 because it was compounded quarterly
t = 12
By substituting these values into the formula,
6500 = PV(1 + 0.059/4)^4 * 12
6500 = PV(1.01475)^48
PV = 6500/(1.01475)^48
PV = 3218.69
I’m getting 57.14 inches for perimeter and 114.29 for area, am I correct? Have struggled a little
Part 1
Find out the perimeter
The perimeter of the figure is given by
[tex]\begin{gathered} P=\pi(8)+8+8 \\ P=16+8\pi \\ P=41.13\text{ in} \end{gathered}[/tex]The perimeter is 41.13 inchespart 2
Find out the area
The area is given by
[tex]\begin{gathered} A=\pi(4^2)+8^2 \\ A=16\pi+64 \\ A=114.27\text{ in2} \end{gathered}[/tex]The area is 114.27 square inches2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.
2) The next day they go to Melties. Al buys a cone with 3.6 oz of frozen yogurt for $4.47, and Beth buys a cone with 4.8 oz of frozen yogurt for $5.01. Find how much Melties charges per ounce of frozen yogurt and how much they charge for the cone.
Let
x ------> the number of ounces of frozen yogurt
y ------> the total charge
we have the ordered pairs
(3.6,4.47) and (4.8,5.01)
step 1
Find the slope pr unit rate
m=(5.01-4.47)/(4.8-3.6)
m=$0.45 per ouncestep 2
Find the equation in point slope form
y-y1=m(x-x1)
we have
m=0.45
(x1,y1)=(3.6,4.47)
substitute
y-4.47=0.45(x-3.6)
convert to slope intercept form
y-4.47=0.45x-1.62
y=0.45x+2.85
In this problem, the y-intercept or initial value correspond to the charge for the cone
so
$2.85