Question: Simplify the expression 1 + 0.25 (8 + 12) - 0.3 × 2
Solution:
Distributing 0.25 in the sum we obtain:
[tex]1\text{ + (0.25x 8 + 0.25 x12) - 0.6}[/tex]Performing each of the operations we obtain:
[tex]1\text{ + (2 + 3) - 0.6}=\text{ 1 + 5 -0.5 = 5.5}[/tex]So the correct answer is
[tex]1+0.25(8+12)-0.3\times2\text{= 5.5}[/tex]The odometer in a car measures the number of miles driven by the car since it was made. During the trip, the odometer in Anita‘s car is modeled by the function Y=9500+55X where X represents the number of hours driven during the trip and y represents the odometer reading in miles. What is the meaning of the rate change in this function?
The given function is y=9500+55x, where x is in hours driven and y is in miles.
Therefore, the slope of the function is
[tex]\frac{miles}{number\text{ of hours driven}}[/tex]The answer is the number of miles driven each hour during the trip, the first option.7
Return
Previous
Ne
10 points
A cylindrical can holds 28 in³ of soup. If the can is 4 in. tall, what is the radius of the can to the nearest tenth of an inch?
Round your answer to the nearest hundredth. Only numbers in your answer.
(Hint: V = πr²h)
V =
type your answer...
h =
type your answer...
r =
type your answer...
The radius of the cylinder is 1.49.
What is a cylinder?
A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance.
These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. The perpendicular distance between the bases is the height, “h” and the distance from the axis to the outer surface is the radius “r” of the cylinder.
Volume of the cylinder can be found with the help of the formula
V = πr²h, where V is the volume of the cylinder, r is the radius and h is the height.
Given,
volume of cylinder = 28
Height of the cylinder = 8
Formula of volume of cylinder is
π[tex]r^{2} h[/tex]= 28
Substitute the values
3.14([tex]r^{2}[/tex])(4)= 28
[tex]r^{2}[/tex] = 28/12.56
[tex]r^{2}[/tex] = 2.22
r = [tex]\sqrt{2.22}[/tex]
r = 1.49
Hence, the radius is given by 1.49 in.
To know more about cylinder, visit:
https://brainly.com/question/15971871
#SPJ9
A graph with the point 6,-5 with a slope of -2/3
The graph of the line y=-2/3x-1 can be given as follows,
What is a equation of ?
The general equation of straight line is y=mx+c where m is the slope and c is the y-intercept.
every point on the line satisfies its equation.
We are given a point (6,-5) and slope -2/3.
we first need to find the equation of the line
y=mx+c
[tex]y=\frac{-2}{3}x+c[/tex]
The point (6,-5) satisfies the equation.
[tex]-5=\frac{-2}{3}(6)+c[/tex]
[tex]-5=-4+c\\c=-1[/tex]
Substituting the value of c in the equation
we get,
[tex]y=\frac{-2}{3}x-1[/tex]
Now we plot the graph of the equation,
To learn more about equation of line please refer
https://brainly.com/question/18831322
#SPJ9
please help 100 points urgent algebra 2
write without using rational exponents
(m^3n^5)^1/4
write out the steps and the answer and please do it right
The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ . ⁴√n⁵.
To solve the expression (m³n⁵)¹/⁴ without using rational exponents
(m)ᵃ/ᵇ = ᵇ√mᵃ
The given algebric expression is (m³n⁵)¹/⁴
As per the Power distribution Formula :
(mᵃnᵃ)ᵇ = mᵃᵇ nᵃᵇ
(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴
We know that
fraction formula : a¹/ⁿ = ⁿ√a
(m)ᵃ/ᵇ = ᵇ√mᵃ
(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴
⁴√m³ x ⁴√n⁵
⁴√m³ . ⁴√n⁵
The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ . ⁴√n⁵.
To learn more about the exponents and powers refer here
https://brainly.com/question/11975096
#SPJ1
the scatter plot shows the results of a survey in which 10 people were asked how many e-mail accounts and how many credit cards they have. how many credit cards does the person with 3 e-mail accounts have?
In the scatter plot, the person with 3 e-mail accounts have 1 credit card.
Define scatter plot.Typically, the relationship between variables is observed and visually displayed using a scatter plot, a type of chart. Dots are used to indicate the variable values. Scatter plots employ Cartesian coordinates to show the values of the variables in a data set because the placement of the dots on the vertical and horizontal axes will reveal the value of each individual data point. Other names for scatter plots are scattergram, scatter graphs, and scatter charts.
The association between two numerical variables measured for the same individuals is displayed in a scatterplot. The values of one variable are plotted on the horizontal axis, and the values of the other variable are plotted on the vertical axis. On the graph, each individual in the data is represented by a point.
To know more about scatter plot, visit:
https://brainly.com/question/3273607
#SPJ4
Write -3.5 as the ratio of two integers
-3.5 number can be written as the ratio -7:2.
We have,
To write -3.5 as the ratio of two integers, we can multiply both the numerator and denominator by 10 to get rid of the decimal point.
This gives us:
-3.5 = -35/10
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.
This gives us:
-3.5 = -7/2
Therefore,
-3.5 number can be written as the ratio -7:2.
Learn more about ratios here:
https://brainly.com/question/2462048
#SPJ1
A basketball player made 74 out of 100 attempted free throws. What percent of free throws was made
Answer:
74%
Step-by-step explanation:
74 divided by 100 is 0.74, and 0.74 =
74%
dillon (2019, unit 2, chapter 14) recommends that the amount of time college students spend studying each week should be about the amount of time spent in class.
Using a proportional relationship, it is found that:
Dillon recommends that the amount of time college students spend studying each week should be about the amount twice the time spent in class.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the rule presented as follows:
y = kx
For this problem, the variables are presented as follows:
Variable x: number of units in class.Variable y: number of hours studied.From the table, the constant is calculated as follows:
k = 24/12 = 18/9 = 12/6 = 2.
Meaning that the amount of study should be twice the time spent in class.
Missing InformationThe table relating the variables is given at the end of the answer.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
Select the equivilent expression(4 ^ 3 / 5 to the negative power of two) ^ 5
A rule that we need to know in order to solve this is:
[tex](a^b)^c=a^{bc}[/tex]The extended rule would be:
[tex](\frac{a^b}{c^d})^x=\frac{a^{bx}}{c^{dx}}[/tex]Also, remember another rule:
[tex]\frac{1}{a^{-x}}=a^x[/tex]Keeping all these rules in mind, we can simplify:
[tex](\frac{4^3}{5^{-2}})^5=\frac{4^{15}}{5^{-10}}=4^{15}\cdot5^{10}[/tex]THis is the final form.
Trevon invests $1650.00 into an account that earns 2% annual interest rate compounded continuously. Assuming no other withdrawals or
deposits, how much will be in the account in 8 years? (Numeric answer only, do not type a $ sign. Round to the nearest cent).
Answer:
1914
Step-by-step explanation:
interest for one year = 33
interest of 8 years = 264
1650+264 will be in the account in 8 years.
Which of the following is the area between a z-score of -0.3 and 0.6?
Answer:
0.34366
Step-by-step explanation:
I'm not 100% sure but that's what I found. also, it says which of the following, so I don't know the answer choices so don't blame me if it's not on the answer choices
Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check a
that apply.
O p(x)=14(x + 7)²+1
O g(x) = -5(x+10)²-1
D s(x) = −(x−1)2 +0.5
O g(x)=2x² +10x-35
Ot(x)=-2x² - 4x-3
The results for the given function are as follows:
1. p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.
2. q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.
3. s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.
4. g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.
5. t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.
What is the function?
In mathematics, the function is an expression or rule, or law which defines the relationship between dependent and independent variable. Functions are ubiquitous and are essential for designing physical relationships.
According to the question, the given function expression as well as transformation results are as follows:
p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.
q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.
s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.
g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.
t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.
By using property of the function which states that if a constant value is added to the function it will go upward, similarly, If we subtract a constant then it will go downward.
To learn more about the function link from the given link:
https://brainly.com/question/25638609
#SPJ13
Suppose corn chips cost 33.5 cents per ounce. if a bag costs $4.35, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
Answer:
13
Step-by-step explanation:
1Given f(x) = 3x and g(x) = x - 2Which value is in the domain of fºg?Click on the correct answer.-225-8
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=3x \\ g\mleft(x\mright)=x-2 \end{gathered}[/tex]We will caculate fºg thus:
[tex]\begin{gathered} fºg=f(g(x))=3(x-2)=\text{3x}-6 \\ fºg=3x-6=0\Rightarrow3x=6\Rightarrow\frac{3x}{3}=\frac{6}{3}\Rightarrow x=2 \\ x=2 \end{gathered}[/tex]Hence, option B is correct
at lone star middle school 2 out of 5 randomly selected students participate in the school science fair if there are 800 students at the middle school how many students will be expected to participate in the science fair.
The number of students that are expected to participate in the science fair is 320.
How many students are expected to participate in the science fair?The ratio of student that participate to the total number of student is 2 : 5. Ratio is used in mathematics to compare two or more numbers together. In this question, for every 5 students, 2 would be chosen to participate in the fair.
In order to determine the number of students that would participate in the fair, multiply the ratio by the total number of students. Multiplication is the process of determining the product of two or more numbers.
Number of students that would participate in the fair = (ratio of students that would participate / total ratio of students) x number of students in middle school
(2 / 5) x 800 = 320 students
To learn more about multiplication, please check: https://brainly.com/question/3385014
#SPJ1
hose a can fill a certain vat in 3 hours. after 2 hours of pumping, hose a is turned off. hose b is then turned on and completes filling the vat in 3 more hours. how long would it take hose b to fill the vat alone?
Time taken by hose B to fill the vat alone = 9 hours
Let 'x' be the capacity of the vat filled in an hour.
Hose A can fill the vat in 3 hours. i.e., 3x quantity is filled in the vat.
After 2 hours of pumping, 2x/3x = 2/3 of the vat is filled.
The remaining to be filled is x/3x = 1/3 capacity of the vat.
It takes 3 hours for hose B to fill the remaining 1/3 capacity of the vat alone.
Let t be the time taken by hose B to fill the whole vat .i.e., 3/3 = 1 capacity of the vat.
In ratio form, 3 : t = 1/3 : 1.
Thus Time taken by hose B to fill the vat alone = 3 ÷ 1/3
= 3 x 3
= 9 hours
Learn more about ratio at https://brainly.com/question/2784798
#SPJ4
0 what number is the dividend in the division problem below? 54 divided by 6 equals 9 A. 9 B.6 C. 54 submit
The dividend in the division problem is 54
How to determine the dividend?The mathematical statement is given as
54 divided by 6 equals 9
The above statement is a quotient expression or quotient statement
A quotient statement is represented as
Dividend divided by Divisor equals Quotient
By comparing the quotient statement with the given mathematical statement, we have the following
Dividend = 54Divisor = 9Quotient= 9This implies that the dividend is 54
Read more about quotient at
https://brainly.com/question/16878818
#SPJ1
Arrange in column then perform the indicated operations. 75 - 26.5731 =
The subtraction is shown below:
The answer is:
75 - 26.5731 = 48.4269
Classwork
Twelve students were given an arithmetic test, and the
times (in minutes) to complete it were
10, 9, 12, 11, 8,15, 9, 7, 8, 6, 12, and 10.
Find:
a) The range
b) Variance and
c) Standard deviation
by using all the values of the data set.
By using all the values of the data set ,
(a) The range for the given set is 9 .
(b) The variance is 6.2045 .
(c) Standard Deviation is 2.49083 .
In the question,
it is given that 12 students gave an arithmetic test , the time (in min) is given as
10, 9, 12, 11, 8,15, 9, 7, 8, 6, 12, 10 .
Arranging the data set in ascending order , we get
6,7,8,8,9,9,10,10,11,12,12,15
Part(a)
the range is calculated by using the formula
Range = highest value - lowest value
Range = 15-6 = 9
Part(b)
calculating , the mean
mean = (6+7+8+8+9+9+10+10+11+12+12+15)/12
= 117/12
= 9.75
Variance can be calculated using the formula
Variance = [tex]\frac{\sum(\(x_i-\bar{x})^{2} }{n-1}[/tex],
where [tex]x_i[/tex] represents the different terms , and
[tex]\bar{x}[/tex] represents the mean .
Substituting the values from the data given , we get
Variance = [(6-9.75)²+(7-9.75)²+(8-9.75)²+(8-9.75)²+(9-9.75)²+(9-9.75)²+(10-9.75)²+(10-9.75)²+(11-9.75)²+(12-9.75)²+(12-9.75)²+(15.9.75)²] / (12-1)
On further simplifying , we get
= 68.25/11
= 6.2045
Part(c)
Standard Deviation = √Variance
Substituting the value of variance from above
we get ,
standard deviation = √6.2045 = 2.49083
Therefore , By using all the values of the data set ,
(a) the range is 9.
(b) Variance is 6.2045
(c) Standard Deviation is 2.49083
Learn more about Variance here
https://brainly.com/question/13112281
#SPJ1
Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
The graphs that give the possible solution to the trigonometric functions are as follows
[tex]1. \ sin(\theta) = \dfrac{-2}{3};\ graphs \ 2\ and \ 3[/tex]
[tex]2. \ sec(\theta) = \dfrac{2}{1};\ graph \ 3[/tex]
[tex]3. \ tan(\theta) = \dfrac{4}{5};\ graph \ 3[/tex]
[tex]4. \ csc(\theta) = \dfrac{-3}{2};\ graph \ 2\ and \ 3[/tex]
[tex]5. \ csc(\theta) = \dfrac{-3}{5}\ graph \ 1[/tex]
What is a trigonometric function?A trigonometric function specifies the relation between two side lengths and an interior angle of a right triangle.
1. The given function is sinθ = -2/3
The definition of sin(θ) is [tex]sin(\theta) = \dfrac{Opposite\ side \ length}{Length \ of \ the \ hypotenuse\ side}[/tex]
From the equation, [tex]sin(\theta) = \dfrac{-2}{3}[/tex], which can be taken as the form, [tex]sin(\theta) = \dfrac{-y}{\sqrt{x^2+y^2} }[/tex], therefore, the opposite side leg, y, will be in the third or fourth quadrant, where the y-value is negative.
The possible graphs are therefore, Graph 2, and Graph 3
2. [tex]sec(\theta) = \dfrac{2}{1}[/tex]
Therefore, [tex]cos(\theta) = \dfrac{1}{2}[/tex]
The definition of cos is [tex]cos(\theta) = \dfrac{Adjacent\ side \ length}{Length \ of \ the \ hypotenuse\ side}[/tex]
Therefore, for the angle in standard position, [tex]cos(\theta) = \dfrac{x}{\sqrt{x^2+y^2} }[/tex]
The adjacent side of the angle is in the positive x-axis, which gives an angle in the Quadrant I or Quadrant IV
The only possible option is graph 3
3. [tex]tan(\theta) = \dfrac{4}{5}[/tex]
The definition of the tangent of an angle is: [tex]tan(\theta) = \dfrac{Opposite\ side \ length}{Length\ of\ the \ Adjacent\ side}=\dfrac{y}{x}[/tex]
Which gives a point at (x, y) or (-x, -y), which are points in Quadrant I and Quadrant III respectively.
The possible solution is therefore graph 3
4. [tex]csc(\theta) = \dfrac{-3}{2}[/tex]
Which gives, [tex]sin(\theta) = \dfrac{-2}{3}[/tex]
Given that the y-value is negative, the possible angle is in Quadrant 3 or 4.
The possible solution is, therefore, graph 2 or 3
5. [tex]cos(\theta) = \dfrac{-3}{5}[/tex]
The x-value is negative; therefore, the angle is in either Quadrant II or Quadrant III
The solution is the graph 1
Learn more about the solutions to trigonometric functions here:
https://brainly.com/question/14421002
#SPJ1
How does the graph of the function g(x)=2|x+7| differ from the graph of the parent function f(x)=|x| ?
a. The graph is translated 7 units to the left. The graph is narrower than the graph of the parent function.
b. The graph is translated 7 units to the left. The graph is wider than the graph of the parent function.
c. The graph is translated up 7 units. The graph is narrower than the graph of the parent function.
d. The graph is translated 7 units to the right. The graph is narrower than the graph of the parent function.
Answer:
Step-by-step explanation:
A
line that has passes through the point (4, 6) and has a slope of 3. Which linear equation models this line?
12x-4=5x+17 please help me solve this equation other conculaters wont help
a boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. if the current is 3 miles per hour, what is the speed of the boat in still water? in still water, the boat travels at miles per hour.
The boat travels at 18 miles per hour.
What is speed?
Speed is calculated as follows: speed = distance / time. Knowing the units for distance and time is necessary to calculate the units for speed.
The rate at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed.
Given: A boat travels 30 miles up the river in the same amount of time it takes to travel 42 miles down the same river. The current is 3 miles per hour.
From the above information we can write,
Let, u is the boat speed in still water, then
[tex]\frac{30}{u-3} = \frac{42}{u+3}[/tex]
Taking cross multiplication,
30(u + 3) = 42(u - 3)
Solving,
30u + 90 = 42u - 126
42u - 30u -126 -90 = 0
12u = 216
u = 18
Therefore, the speed of boat in still water is, 18 miles per hour.
To know more about the speed, click on the link
https://brainly.com/question/13943409
#SPJ4
Bekah has a rectangular garden. The length and width are different odd number
measures, and the perimeter is 12 feet. What is the area of her garden?
Answer:
Step-by-step explanation:
Equationi
2x+1 + 2y+1 = 12 The +1 guarantees that the number is odd. 2x makes any integer even.
Givens
L = 2x + 1
W = 2y + 1
The problem is that you do not have a second equation. So you can just choose.
2x + 1 + 2y + 1 = 12 Combine the left
2x + 2y + 2 = 12 Subtract 2 from both sides
2x + 2y + 2 - 2 = 12 - 2
2x + 2y = 10
x = 3
y = 2
======
x = 2
y = 3
======
L= 3*2 + 1
w = 2*2 + 1
L = 7
w = 5
I don't think there is another solution. The negatives cannot be used because a length or width cannot be (say)
x = - 5
y = 11
Can you measure something that is - 5 units long? Not in this lifetime.
A concert hall is having a special. If a group of five pays $6.75 each for tickets, each person can get a snack for $4.25. Use the expression 5(6.75+4.25) to find the total cost for 5 friends?
Answer: The total cost is $55
The total cost of 5 friends is $55.
What is multiplication?
Multiplication is a basic arithmetic function in which occurs when we add a number a particular number of times.
We are given that if group of five pays $6.75 each they get the snack for $4.25.
To find the total cost we first find the cost of one
The cost of one can be given as [tex]6.75+4.25=11[/tex]
To find the cost of 5 we multiply this amount by 5
We get,
[tex]5[/tex]·[tex]11=55[/tex]
Hence the total cost is $55.
To learn more about the multiplication please refer
https://brainly.com/question/10873737
#SPJ9
8 Select the correct answer. Which inequality represents all the solutions of 10(3x + 2) > 7(2x - 4)? ОА. X> 4 OB. X
The given inequality is expressed as
10(3x + 2) > 7(2x - 4)
The first step is to open the brackets on each side of the inequality by multiplying the terms outside the bracket by the terms inside. Thus, we have
10 * 3x + 10 * 2 > 7 * 2x - 7 * 4
30x + 20 > 14x - 28
Collecting like terms, we have
30x - 14x > - 28 - 20
16x > - 48
Dividing both sides by 16, it becomes
16x/16 > - 48/16
x > - 3
Plllllllllllllllllllllllllllllllllllllllls ANSWER my. My brother need help
Please help you got ten min
DO IT STEP BY STEP
Step-by-step explanation:
Help! Homework: 3x-(1/3x +1)=
Answer:
39/98=90 so its 90
Step-by-step explanation:
you have to add the angles and to make sure to look at each corners of the angles for the answer
