Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
we have that
total distance=4 1/2 miles
Let
x ----> number of miles walked
so
4 1/2=3 5/8+x
solve for x
But first, convert mixed number to an improper fraction
4 1/2=4+1/2=9/2
3 5/8=3+5/8=29/8
substitute
9/2=(29/8)+x
x=(9/2)-29/8
the fractions have different denominators
so
Find out an equivalent fraction
9/2=(9/2)*(4/4)=36/8
so
x=(36/8)-29/8
x=7/8
the answer is 7/8 milesJenna can spend at most $200 on school clothes which inequality represents the amount that Jenna can spend on clothes
x is the quantity Jenna spend on clothes
[tex]x\le200[/tex]what is the volume of the right prism shown ? the prism is drawn to scale . the volume of the prism is _______
The formula to find the volume of a right trapezoidal prism is
[tex]\begin{gathered} V=\frac{(a+b)}{2}\cdot h\cdot l \\ \text{ Where V is the volume} \\ a\text{ is the long base} \\ \text{b is the short base} \\ h\text{ is the height and } \\ l\text{ is the length of the right trapezoidal prism} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} a=7.5in \\ b=5in \\ h=6in \\ l=8in \end{gathered}[/tex][tex]\begin{gathered} V=\frac{(a+b)}{2}\cdot h\cdot l \\ V=\frac{(7.5in+5in)}{2}\cdot6in\cdot8in \\ V=300in^3 \end{gathered}[/tex]Therefore, the volume of the right trapezoidal prism is 300 cubic inches.
Answer:
the volume of the right trapezoidal prism is 300 cubic inches.
Step-by-step explanation:
QRST is a rectangle. Find the value of x and the length of each diagonal. QS = 5x + 12 and RT = 6x – 2
We can draw the rectangle QRST as:
The two diagonals of a rectangle will have the same length, so we can write:
[tex]\begin{gathered} QS=RT \\ 5x+12=6x-2 \\ 5x-6x=-2-12 \\ -x=-14 \\ x=14 \end{gathered}[/tex]With the value of x, we can calculate the length of the diagonal:
[tex]QS=5x+12=5\cdot14+12=70+12=82[/tex]Answer: the lengths of the diagonals QS and RT is 82.
The value of x is 14 and the length of each diagonal would be 82 units.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that QRST is a rectangle.
We have to determine the value of x and the length of each diagonal.
QS = 5x + 12 and RT = 6x – 2
Because a rectangle's two diagonals will be the same length, we may write:
QS = RT
5x + 12 = 6x – 2
Rearrange the terms in the above equation,
6x - 5x = 12 + 2
x = 14
The value of x is 14.
So, QS = 5(14) + 12 and RT = 6(14) – 2
So, QS = RT = 82
Therefore, the length of each diagonal would be 82 units.
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Given the triangle ABC at points A = ( 1, - 4 ) B = ( 4, - 5 ) C = ( 6, - 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.
Given: The coordinates of triangle ABC as
[tex]\begin{gathered} A=(1,-4) \\ B=(4,-5) \\ C=(6,-3) \end{gathered}[/tex]To Determine: The coordinates of triangle ABC after first reflect over the y-axis and then over the x-axis
Solution
The reflection over the y-axis rule is given as
[tex](x,y)\rightarrow(-x,y)[/tex]Let us apply the rule to the given triangle ABC
[tex]\begin{gathered} A(1,-4)\rightarrow A^{\prime}(-1,-4) \\ B(4,-5)\rightarrow B^{\prime}(-4,-5) \\ C(6,-3)\rightarrow(-6,-3) \end{gathered}[/tex]The reflection rule over the x-axis is given as
[tex](x,y)\rightarrow(x,-y)[/tex]Let us apply the rule to the given
[tex]\begin{gathered} A^{\prime}(-1,-4)\rightarrow A^{\prime}^{\prime}(-1,4) \\ B^{\prime}(-4,-5)\rightarrow B^{\prime}^{\prime}(-4,5) \\ C^{\prime}(-6,-3)\rightarrow C^{\prime}^{\prime}(-6,3) \end{gathered}[/tex]Hence, the new point of A'' = (-1, 4)
what is 10 reproduced at a 1/2 scale
Scaling
To scale a number by a certain amount, multiply both quantities.
The number 10 reproduced at a 1/2 is:
[tex]\begin{gathered} 10\cdot\frac{1}{2} \\ =\frac{10}{2} \\ =5 \end{gathered}[/tex]Answer: 5
Find the volume of the cone to the nearest 10th power you use 3.14 for pi. In the second box, take the exponent for the label.
The volume of a cone of radius r and height h is given by:
[tex]V=\frac{\pi r^2h}{3}[/tex]The cone in the figure has a radius of r = 2.1 cm and a height of h = 6.2 cm.
Substituting:
[tex]V=\frac{\pi\times\lparen2.1cm)^2\times6.2\text{ cm}}{3}[/tex]Using the value 3.14 for pi and calculating:
V = 28.62 cm 3
You should write 28.62 in the first box and 3 in the second box (for cubic cm)
Help please. I’ve had health issues recently and i’m trying to catch up on work and learn it. Thank you so much
80 mililiters of the 10% solution
120 mililiters of the 30% solution
Explanation:
let the amount of solution for the 10% = x
let the amount of solution for the 30% = y
The sum of the amount for the mixture of 10% solution and amount for the 30% solution = 200 mililiters
x + y = 200 ...(1)
In terms of fraction for each solution:
fraction of the 10% solution + fraction of the 30% solution = fraction of the mixture
percentage of the solution of the mixture = 22%
fraction of the 10% solution = 10% (x) = 0.1(x) = 0.1x
fraction of the 30% solution = 30%(y) = 0.3(y) = 0.3y
fraction of the mixture = 22%(200) = 0.22(200)
substitute the above into the equation for fraction:
0.1x + 0.3y = 0.22(200)
0.1x + 0.3y = 44 ...(2)
combine both equatons:
x + y = 200 ...(1)
0.1x + 0.3y = 44 ...(2)
Using substitution method to solve the equations:
from equation 1, let's make x the subject of formula:
x = 200 - y
substitute for x in equation (2):
0.1(200 - y) + 0.3y = 44
20 - 0.1y + 0.3y = 44
20 + 0.2y = 44
0.2y = 44 - 20
0.2y = 24
divide both sides by 0.2:
0.2y/0.2 = 24/0.2
y = 120
sustitute for y in equation (1):
x + 120 = 200
x = 200 - 120
x = 80
Hence, James must mix:
80 mililiters of the 10% solution
120 mililiters of the 30% solution
Please Help. Functions and Relations. What is the effect on the graph of f(x)= x^2 when it is transformed to h(x)= 2x^2 + 15??
In general, given a function g(x), a vertical stretch/compression is given by the transformation below
[tex]\begin{gathered} g(x)\rightarrow a*g(x) \\ a>1\rightarrow\text{ stretch} \\ 0Therefore, in our case,[tex]x^2\rightarrow2x^2\Rightarrow\text{ vertical stretch by a factor of 2}[/tex]On the other hand, a vertical shift is given by the following transformation
[tex]\begin{gathered} g(x)\rightarrow g(x)+b \\ b>0\rightarrow\text{ b units up} \\ b<0\rightarrow\text{ b units down} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} 2x^2\rightarrow2x^2+15=h(x)\Rightarrow\text{ 15 units up} \\ \end{gathered}[/tex]Hence, the answer is option C. Vertical stretch by a factor of 2 and a vertical shift by 15 units up.Solve 3n - 5p + 2n = 10p for n.
Solving for n ,
[tex]\begin{gathered} 3n-5p+2n=10p \\ \rightarrow3n+2n=10p+5p \\ \rightarrow5n=15p \\ \rightarrow n=\frac{15p}{5} \\ \\ \Rightarrow n=3p \end{gathered}[/tex]you pick a card at random and put it back and then pick another card at random what is the probability of picking an even number and then picking a five
STEP - BY - STEP EXPLANATION
What to find?
The probability of picking an even number and then picking a five.
Given:
Step 1
State the probability formula.
[tex]Probability=\frac{required\text{ outcome}}{all\text{ possible outcome}}[/tex]Step 2
Identify the even numbers and the all possible outcome.
Even numbers =4, 6
Step 3
Find each of the probability.
Let A be the event of picking an even number and B be the event of picking a 5.
[tex]\begin{gathered} P(A)=\frac{2}{4} \\ \\ P(B)=\frac{1}{4} \end{gathered}[/tex]Step 4
Determine the compound probability.
[tex]\begin{gathered} P(A\text{ and B\rparen=P\lparen A\rparen}\times P(B|A) \\ \\ =\frac{2}{4}\times\frac{1}{4} \\ \\ =\frac{2}{16} \\ \\ =\frac{1}{8} \end{gathered}[/tex]Step 5
Convert to percentage.
[tex]\begin{gathered} Probability=\frac{1}{8}\times\text{ 100\%} \\ \\ =12.5\text{ \%} \end{gathered}[/tex]ANSWER
12.5 %
A pitcher has the ability to throw a baseball at 95 mph.a. How fast is the speed in ft/s? b. How long does the hitter have to make a decision about swinging at the ball if the plate and the mound are sepa- rated by 60 ft? c. If the batter wanted a full second to make a decision, what would the speed in mph have to be?
Speed = 95 miles per hour
a. to express it in feet per second
1 mile = 5280 ft
1 hour = 3600 seconds
(95 x 5280 )/3600 = 139.33 ft/s
b. Speed = distance / time
Time = Distance / speed
Distance = 60ft
Time = 60ft / 139.33 ft /s = 0.43 seconds
c.
speed= distance / time
S = 60 ft / 1 sec = 60 ft/s
you can have more than one point slope equation for a single line. true or false?
Given:
Any single line can have more than one point-slope equation.
To check: It is true or false.
Explanation:
The standard form of a point-slope equation is,
[tex]y=mx+c[/tex]Where m is the slope of the line and c is the y-intercept.
Here, (x, y) is any one point of the line.
The slope of the line is the same for every point of the line. Also, there must be a single y-intercept since the straight line has a linear function.
Any single line can have more than one point-slope equation if we change points simultaneously.
That is,
At every point of the line, we can write the point-slope eq
Solve using substitution.y = -x - 1y = x + 3Submit
y = -x - 1 (a)
y = x + 3 (b)
Replace the value of y in the first equation (a) by the value of y in the second equation (b).
x+3=-x-1
Solve for x
x+x=-1-3
2x=-4
x=-4/2
x= -2
Replace the value of x in (a) or (b)
y=-x-1
y= -(-2)-1
y= 2-1
y=1
g(x)=14-2/3x and h(x)= -x-7
Solve g(9)+h(-14)
The value of the addition function is found as g(9) + h(-14) = 565/27.
What is defined as the domain of the function?A is a mathematical entity that accepts input, relates a rule to it, and returns the result. The domain of a function is the collection of all its inputs. Its codomain is the collection of all possible outputs. The range refers to the outputs which are actually used.For the given question,
The functions are given as;
g(x)=14-2/3x and h(x)= -x-7
Find the value of the function for the given domain of g(9) and h(-14).
g(9); Put x = 9 in g function.
g(9) = 14-2/3×9
g(9) = 376/27
h(-14); Put x = -14 in function h.
h(-14) = -x-7
h(-14) = -(-14)-7
h(-14) = 7
Now, add both values;
g(9) + h(-14) = 376/27 + 7
g(9) + h(-14) = 565/27
Thus, the value of the addition function is found as g(9) + h(-14) = 565/27.
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What is the conjugate of −1−5i?
The conjugate will be -1 + 5i
Explanation:Given:
[tex]-1\text{ - 5i}[/tex]To find:
the conjugate of the above complex number
A complex number is in the form: a + bi
The conjugate of the complex number is a - bi
When the complex number is -1 - 5i, where a = -1, b = -5i
The conjugate will negate the value of b
a will be -1 while b = -(-5i) = 5i
The conjugate will be -1 + 5i
Which expression is equivalent to 5(24 - 9)?(5×24)-(5×9)(5×24)+(5×9)(5×24)-9(5×24)+9
5 ( 24 - 9 )
= ( 5 X 24 ) - ( 5 X 9 ) ----------- OPTION A
simplifying fractions 35/45
Given the fraction: 35/45
We will simplify the fraction as follows:
[tex]\frac{35}{45}=\frac{5\cdot7}{5\cdot9}=\frac{7}{9}[/tex]LCM for 35 and 45 is 5
So, divide both numbers by 5
It takes approximately 4.65 quarts of milk to make a pound of cheese. Express this amount as a mixed number in simplest form.
The amount of the quarts of milk to prepare a pound of cheese in mixed number is 4 ¹³/₂₀.
What is the meaning of the term mixed number?The mixed number is a representation of both a whole number and a legal fraction. A whole number, one numerator, as well as a denominator are combined to create a mixed number.Creating mixed fractions from incorrect fractions.
Step 1: Divide this numerator by the denominator
Step 2: The quotient should be expressed as a whole number.
Step 3: Input the numerator and denominator as the remainder and the divisor, respectively.
For the given question,
The quantity of 4.65 quarts of milk to make a pound of cheese.
This can be written as-
= 465/100
Dived the numerator and denominator by 5
= 93/20
Write the value in mixed fraction as;
The remainder will be 13 after diving 93 with 20 and with quotient 4.
= 4 ¹³/₂₀.
Thus, the amount of the quarts of milk to prepare a pound of cheese is 4 ¹³/₂₀.
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > - 2 x - 7
In order to determine a point that is part of the solution of the two given inequality, let's graph the two inequalities.
For both inequalities, they are already in a slope-intercept form y > mx + b where m = slope and b = the y-intercept.
For equation 1, y > x + 2, the y-intercept is 2 and slope is 1. Since the inequality is >, we will be using a broken line and the shade will be above the line.
The graph of inequality 1 is:
Moving on inequality 2, y > -2x - 7, the slope is -2 and the y-intercept is -7. Since the inequality symbol is >, we will be using a broken line on its border and the shade will be above the line.
The graph of inequality 2 is:
Combining the two graphs in one coordinate plane, we have:
The solution set of the given system of inequalities will be the common shaded area of both inequalities. There are infinite solutions for this.
We can get some coordinates from this common shaded area and this could be:
These coordinates can be (-3, 2), (-4, 3), (-2, 4), or (-2, 2).
We can also infer from the graph that the value of x is infinite however, the value of y must be greater than -1.
Warren buys a bag of cookies that contains 5 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cookies.What is the probability that Warren reaches in the bag and randomly selects 2 peanut butter cookies from the bag? Round your answer to four decimal places. Hint: Did you use conditional probability?
ANSWER
0.0593
EXPLANATION
The total number of cookies in the bag is,
[tex]5+6+6+6=23[/tex]When Warren takes the first cookie, the probability of it being a peanut butter cookie is 6 out of 23,
[tex]P(pb_1)=\frac{6}{23}[/tex]If the first cookie was peanut butter, when he takes the second cookie there are only 5 peanut butter cookies left and a total of 22 cookies, so the probability of that second cookie being peanut butter is,
[tex]P(pb_2)=\frac{5}{22}[/tex]So, the probability that Warren selects 2 peanut butter cookies from the bag is,
[tex]P(2pb)=\frac{6}{23}\times\frac{5}{22}\approx0.0593[/tex]Hence, the probability that he takes 2 peanut butter cookies is 0.0593.
What Is the difference between 4×3 and 4^3 ? Prove your answer with the equations AND explain your thinking.
The given expressions are
4×3 and 4^3
4 x 3 means 4 multiplied by 3 and the result is 12
4^3 means 4 raised to the power of 3 and this means
4 muliplied by 4 multiplied by 4. Thus, we have
4 x 4 x 4 = 64
guys whatd 3/2000 please help this is due by tomorrow
Answer:
0.0015
Step-by-step explanation:
don't forget to follow rate like
Find the Least Common Denominator of 1/4 and 5/6
Answer:
The Least Common Denominator of 1/4 and 5/6 is 12
Explanation:
The Least Common Denominator (LCD) of two fractions is smallest number that can be common denominator for the set of fractions.
Given 1/4 and 5/6
The denominators are:
4 and 6
Let us break each numbers down into multiplications of prime numbers
4 = 1 * 2 * 2
6 = 1 * 2 * 3
So, the LCD is: 1 * 2 * 2 * 3 = 12
what is the equation of the line passing through the points (-2,3) and (1,4)?
Solution:
Given the points below;
[tex]\left(-2,3\right)\text{ }and\text{ }(1,4)[/tex]To find the equation of a straight line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(-2,3) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]Substitute the values of the coordinates into the formula to find the equation of a straight line above
[tex]\begin{gathered} \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \frac{y-3}{x-(-2)}=\frac{4-3}{1-(-2)} \\ \frac{y-3}{x+2}=\frac{1}{1+2} \\ \frac{y-3}{x+2}=\frac{1}{3} \\ Crossmultiply \\ 3(y-3)=1(x+2) \\ 3y-9=x+2 \\ x+2=3y-9 \\ x+2-(3y-9)=0 \\ x+2-3y+9=0 \\ x-3y+2+9=0 \\ x-3y+11=0 \end{gathered}[/tex]Hence, the general equation of the line is
[tex]x-3y+11=0[/tex]Mikaela has been tracking her basketball stats for the last week. She started shooting hoops today having already made 3200 baskets thisweek. She tracks how many baskets she has made in the next 30 minutes. If she continues shooting, how many baskets will she have made ifshe continues for one hour today? Write a linear equation with the variablet for time, then solve for the number of baskets.start 320010 min 322520 min 325030 min 327540 min 3300
Given:
Mikaela has been tracking her basketball stats for the last week.
We need to write a linear equation with the variable t for time
Let the equation has the form: y = m * t + b
Where y is the number of baskets she has made
She started shooting hoops today having already made 3200 baskets this
week.
so, at t = 0 , y = 3200
so, the value of b = 3200
We will find the value of m using the given table:
start 3200
10 min 3225
20 min 3250
30 min 3275
40 min 3300
So, the value of m = (3250 - 3225)/(20 - 10) = 25/10 = 2.5
So, the equation will be:
[tex]y=2.5t+3200[/tex]Now, we will find how many baskets will she have made if
she continues for one hour today?
So, we will substitute with t = 60 min into the last equation
So,
[tex]y=2.5\cdot60+3200=3350[/tex]So, she will make 3350 baskets
Use the factor theorem to determine if( x - 2) + (x + 4) are factors of the function below
Here, the dividend is x^3-6x^2+11x+6 and the divisor is x-2.
Put the value of divisor as 0 implies,
[tex]\begin{gathered} x-2=0 \\ x=2 \end{gathered}[/tex]Find f(2) implies,
[tex]\begin{gathered} f(2)=2^3-(6\times2^2)+(11\times2)-6 \\ =8-24+22-6 \\ =0 \end{gathered}[/tex]Therefore, x-2 is a factor of the polynomial.
Pu the value 0 for x+4 gives,
[tex]\begin{gathered} x+4=0 \\ x=-4 \end{gathered}[/tex]Find f(-4) gives,
[tex]\begin{gathered} f(-4)=(-4)^3-(6\times(-4)^2)+(11\times-4)-6 \\ =-64-96-44-6 \\ =-210 \end{gathered}[/tex]Therefore, x+4 is not a factor of polynomial.
Hence, Option C.
Karen runs each lap in 7 minutes. She will run less than 63 minutes today. What are the possible numbers of laps she will run today? Use n for the number of laps she will run today. Write your answer as an inequality solved for n.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
time for each lap = 7 min
today's time run less than 63 min
n = # laps
Step 02:
1 lap ------- 7 min
n laps ------ 63 min
n laps * 7 min = 1 lap * 63 min
n laps < 63 min * lap / 7 min
n laps < 9 laps
The answer is:
She will run less than 9 laps .
Question is shown in image below. Answer format is also shown in image.
For |2x-7|>1:
This absolute value inequality results in two inequalities: 2x-7>1 or 2x-7<-1.
Solve these inequalities to find the answer:
[tex]\begin{gathered} 2x-7>1 \\ 2x>1+7 \\ x>\frac{8}{2} \\ x>4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7<-1 \\ 2x<-1+7 \\ x<\frac{6}{2} \\ x<3 \end{gathered}[/tex]It means that the answer is x>4; x<3.
For |2x-7|<1:
This results in one complex inequality: -1<2x-7<1.
Solve it to find the answer:
[tex]\begin{gathered} -1<2x-7<1 \\ -1+7<2x<1+7 \\ 6<2x<8 \\ \frac{6}{2}It means that the answer is 3For |2x-7|=1:From the equation we can conclude that 2x-7=1 or 2x-7=-1.Solve these equations to find the answer:[tex]\begin{gathered} 2x-7=1 \\ 2x=1+7 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} 2x-7=-1 \\ 2x=-1+7 \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]The answer is x=3; x=4.The average gas price in 2013 was $3.34. The probability that a gas price was less than $2.90 was 20%. What would be the standard deviation?
We know that the probability in a normal distribution can be obtained by the z score, the z score is given as:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where mu is the mean and sigma is the standard deviation. In this case we have:
[tex]\begin{gathered} P(X<2.9)=0.2 \\ P(Z<\frac{2.9-3.34}{\sigma})=0.2 \\ P(Z<\frac{-0.44}{\sigma})=0.2 \end{gathered}[/tex]Now, to have 20% (that is 0.2) we need that the z score to be -0.842, then we have:
[tex]\begin{gathered} -\frac{0.44}{\sigma}=-0.842 \\ \sigma=\frac{-0.44}{-0.842} \\ \sigma=0.52256532 \end{gathered}[/tex]Therefore the standard deviation is $0.52
-5m=8m-2 what solution? one solution.. two solutions... no solutions.. infinite solutions.. which solution?
Starting with the equation:
[tex]-5m=8m-2[/tex]Substract 8m from both sides:
[tex]\begin{gathered} -5m-8m=8m-2-8m \\ \Rightarrow-13m=-2 \end{gathered}[/tex]Divide both sides by -13:
[tex]\begin{gathered} \frac{-13m}{-13}=\frac{-2}{-13} \\ \Rightarrow m=\frac{2}{13} \end{gathered}[/tex]Therefore, the equation has one solution, which is:
[tex]m=\frac{2}{13}[/tex]