2 to the power of 5 can be written as
[tex]$2^{5}[/tex] = 2 2 2 2 2 2 = 32. Power is defined as a base number multiplied by its exponent, where the base number is the factor multiplied by itself and the exponent is the number of times the same base number is multiplied.
What is meant by second power?The number 5³ is pronounced as "five to the third power," "five to the power three," or "five to the third." There are two special powers: "to the second power" is commonly pronounced "squared," and "to the third power" is commonly pronounced "cubed."To find ax, simply multiply a by itself x times. To compute two to the second power, multiply two by itself two times. The exponent of a number indicates how many times the number should be multiplied. The "2" in 8² tells us to multiply 8 twice, so 8² = 8 × 8 = 64. In other words, 8² could be referred to as "8 to the power 2," "8 to the second power," or simply "8 squared."To learn more about exponent, refer to:
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if there is a rectangle and the smaller side is 3 and the area is 27 what is the other side length
Answer:
Area of rectangle is given as length x breadth/width, where the length is the longer side and the breadth/width is the shorter side.
Let length be l.
l x 3 = 27
l = 27 ÷ 3
= 9
Write the equation of a line that passes through (3,21) and has a slope of 3
Answer:
y = 3x + 12
Step-by-step explanation:
so the point slope form of an equation is is y minus y1 = M (x - X1) where why one equals the first point Y value and X1 is the first point x value and M equals the slope . if you substitute your question into this equation you will you will get y - 21 = 3 ( x - 3).
if you want to be fancy haha you can put this into the linear equation form y = mx + b so then you can add 21 to the other side to get y=3(x-3)+21. after that you foil and get y equals 3x - 9 + 21 . simplify and you get why equals 3x + 12
Using the law of sines, determine whether the given information results in one triangle, two triangle or no triangle at all. Solve any triangle that results. a=8angle B = 57 degreeAngle A =49 degree
step 1
Find out the measure of angle C
Remember that
In any triangle, the sum of the interior angles must be equal to 180 degrees
so
A+B+C=180 degrees
substitute given values
49+57+C=180
C=180-106
C=74 degrees
step 2
Find out the length side b
Applying the law of sines
[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]substitute
[tex]\frac{8}{s\imaginaryI n49^o}=\frac{b}{s\imaginaryI n57^o}[/tex]Solve for b
[tex]\begin{gathered} b=\frac{8*s\mathrm{i}n57^o}{s\imaginaryI n49^o} \\ \\ b=8.89\text{ ---> rounded to two decimal places} \end{gathered}[/tex]step 3
Find out the length side c
Applying the law of sines
[tex]\frac{a}{s\imaginaryI nA}=\frac{c}{s\imaginaryI nC}[/tex]substitute
[tex]\frac{8}{s\imaginaryI n49^o}=\frac{c}{s\imaginaryI n74^o}[/tex]solve for c
[tex]\begin{gathered} c=\frac{8*s\mathrm{i}n74^o}{s\imaginaryI n49^o} \\ \\ c=10.19\text{ ----> rounded to two decimal places} \end{gathered}[/tex]therefore
N of triangles is only oneb=8.89c=10.19C=74 degrees
The sum of two numbers is 450. The larger number is 50 more than three times the smaller
number. What are the two numbers?
Answer: 100 and 350
Step-by-step explanation:
Let x be the smaller one.
Based on the second statement, [tex]3x + 50[/tex] is the larger one.
[tex]x + 3x + 50 = 4x + 50 = 450; x = 100[/tex]
Based on that, the larger one is 450 - 100 = 350
A student needs at least seven hours of sleep each night. The student goes to bed at 11:00pm and wakes up before 6:30am. Is the student getting enough sleep? Write an inequality for the number of hours of sleep the students gets each night
The student is getting enough sleep because the student is sleeping for 7 hours 30 minutes. The inequality for the number of hours of sleep is x ≥ 7 hours.
What is the inequality?For the student to be getting enough sleep, the student has to sleep for greater than 7 hours. The first step is to determine the number of hours slept.
In order to determine the time the student spent sleeping, subtract the time he slept from the time he woke up. Subtraction is the process that is sued to determine the difference between two or more numbers.
The sign that represents subtraction is -. In this case, 6 : 30am - 11 : 00pm = 7 hours 30 minutes. The sign to use is ≥ because the student can sleep for 7 hours or greater.
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The student is getting enough sleep.
The inequality that represents the number of hours a student should sleep each night is s ≥ 7 hours.
What is the inequality?In order to determine if the student is getting enough sleep, we have to determine the total hours between 11:00pm and 6:30am. The total hours between 11:00pm and 6:30am is 7 hours 30 minutes. 7 hours 30 minutes is greater than 7 hours. Thus, the student is getting enough sleep.
Here are inequality signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The sign that would be used is, ≥ , the greater than or equal to sign
The total hours slept ≥ 7 hours
s ≥ 7 hours
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How much is the sales tax?
Price $24.95
Tax 7%
price x.0%= tax
Show Work!
Therefore the sales tax is $ 1.7465.
A percentage is what?Another approach to express fractions is in percentages, where the denominator is 100. (percent). 'Percent' literally means 'out of 100. For instance, 20% denotes one out of every five because five twenty-dollar bills can fit in a hundred. A percentage can occasionally be expressed as a decimal, with 100% being the same as 1. As an illustration, 0.68 is equal to 68%.
Given:
Price $24.95
Tax 7%
Therefore 7% of $24.95
= $ 7/100 x 24.95
= $ 1.7465
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f(x) = x - 5; g(x) = f(x − 3)
Answer:
g(x) = x - 8
Step-by-step explanation:
f(x) = x - 5
g(x) = f(x-3) = f(x-5) - 3 = x -8
Solve for d.
d
3
+ 23
= 28
Answer:
what ?????? any more information about solving for d
What does the following histogram tell us about the scores on the Unit 1 Exam?
A most students scored 95% on the exam.
B The mean of all the scores was 70%
C most students scored in the 80-90 range
D the highest score on the exam was 100
The frequency counts of values for the various levels of a nominal or categorical variable are displayed in bar charts. Bar graphs can also display additional statistics, including percentages. A sample bar chart for survey response data
Explain about bar chart?
When you have at least one category or discrete variable, use bar charts to compare categories. Longer bars denote greater values, and each bar represents a summary value for one discrete level. Counts, sums, averages, and standard deviations are a few examples of summary values. Bar graphs are another name for bar charts.
A bar graph is a visual tool that employs bars to compare data between categories. It is sometimes referred to as a bar chart or bar diagram. A bar graph can be vertically or horizontally oriented. It's crucial to understand that a bar's value increases with length.
Most students scored in the 80-90 range
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Calculate the rise and run to find the slope of each line! Please help me!!!
Answer:
m = - ( 1 / 4 )
Step-by-step explanation:
Slope is rise over run.
y = mx + c;
m = ( Δy / Δx );
They give us two points (-4, 3) and (4, 1).
The change is the difference.
Δy = 3 - 1 = 2;
Δx = -4 - 4 = -8;
m = ( 2 / -8 );
m = -( 1 / 4 );
Negative Quarter
Which equation written below in vertex form is equivalent to the equation?
First, consider that a quadratic equation in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]where a is the leading coefficient and (h,k) is the vertex of the curve.
You have the following equation:
[tex]y=x^2-6x+12[/tex]In this case, the leading coefficient is a = 1.
The vertex is determined as follow:
Use the following formula to find h:
[tex]h=-\frac{b}{2a}=-\frac{-6}{2(1)}=3[/tex]where we have used b = -6.
Now, to find k use:
[tex]f(h)=(3)^2-6(3)+12=9-18+12=3[/tex]Then, h = 3 and k = 3.
By replacing the values of a, h and k, you obtain:
[tex]y=(x-3)^2+3[/tex]The previous result is the given equation in vertex form.
A pilot takes a taxi from the airport to a hotel. The taxi driver charges a $4.50 initial charge plus $1.65 per mile. Write an equation that can be used to find y, the total cost of the trip, if x represents the number of miles of the trip?
y = 1.65x + 4.50
Step-by-step explanation:We can create a linear equation using the variables given to us to represent this situation.
Linear Equations
Most linear equations are written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept.
In context, slope is the cost per mile. That is because the number of miles in the variable in this equation and the cost per mile is the rate at which the variable increases. The y-intercept is the initial charge. That is because the total cost starts a $4.50, even if you haven't gone anywhere yet. Additionally, the initial cost does not change at any point, so it should be a constant.
So, now we can plug the values into slope-intercept form to create a linear equation. (Remember m = 1.65 and b = 4.50)
y = 1.65x + 4.50Solving the Equation
Now that we set up the equation we can solve for y, at different x-values. This means, given the number of miles, we can find the total cost of the trip. We can do this by substituting x-values into the equation.
For example, let's say that a pilot took a 4-mile taxi ride.
First, plug 4 in for x.
y = 1.65(4) + 4.50Then, simplify.
y = 6.6 + 4.50Finally, add the terms together.
y = 11.1This means if a pilot takes a 4-mile taxi ride, then it will cost $11.10.
What is the value of the expression −51 − 17 − (−37)?
−68
−105
−31
−71
please get it right, I'll give you brainliest!
Answer:
c) -31
Step-by-step explanation:
Given expression,
→ -51 - 17 -(-37)
Let's solve the expression,
→ -51 - 17 -(-37)
→ -51 - 17 + 37
→ -51 + 20 = -31
Hence, the answer is -31.
3n³ - 12n²-30n what Is the answer
Step-by-step explanation:
Factor 3n³−12n²−30n
3n³−12n²−30n
=3n(n²−4n−10)
A grocer wants to mix two kinds of coffee. One kind sells for $1.20 per pound, and the other sells for $2.35 per pound. He wants to mix a total of 24 pounds and sell it for$1.65 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
Let be "x" the amount of coffee that is sold for $1.20 per pound (in pounds) that the grocer should use in the new mix and "y" the other kind of coffee that is sold for $2.35 per pound (in pounds) that the grocer should use in the new mix
Using the information given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}x+y=24 \\ 1.20x+2.35y=24\cdot1.65\end{cases}[/tex]Simplifying, you get:
[tex]\begin{cases}x+y=24 \\ 1.20x+2.35y=39.6\end{cases}[/tex]You can solve the system as follows:
1. Multiply the first equation by -1.20.
2. Add the equations.
3. Solve for "y".
Then:
[tex]\begin{gathered} \begin{cases}-1.20x-1.20y=-28.8 \\ 1.20x+2.35y=39.6\end{cases} \\ ------------- \\ 1.15y=10.8 \\ y=9.39 \end{gathered}[/tex]4. Substitute the value of "y" into the first equation.
5. Solve for "x".
Then:
[tex]\begin{gathered} x+9.39=24 \\ x=24-9.39 \\ x\approx14.61 \end{gathered}[/tex]Therefore, the answer is: About 14.61 pounds of the kind of coffee that is sold for $1.20 and about 9.39 pounds of the other kind of coffee that is sold for $2.35 per pound.
(Solving Two-Step Equations MC)
Solve the equation for v.
v over 6 minus 3 equals negative 11
v = 24
v = 63
v = −48
v = −84
Solving the equation, v/6 - 3 = -11, for v, the value of v = -48.
How to Solve an Equation?To solve a given equation, we are required to find the value of the variable in the equation that would make the equation true.
To solve for the variable in an equation, we would need to apply the right properties of equality in other to isolate the variable towards one side of the equation to get the value of the variable.
Given the equation, v/6 - 3 = -11:
v/6 - 3 = -11
Add 3 to both sides
v/6 - 3 + 3 = -11 + 3 [addition property of equality]
v/6 = -8
Multiply both sides by 6
v/6 × 6 = -8 × 6 [multiplication property of equality]
v = -48
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1/3+4.1 Write your answer as a mixed number in simplest form.
4[tex]\frac{13}{30}[/tex] is the solution of equation as a mixed number in simplest form.
Define mixed fraction.A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction. Arithmetic. a number, such as 412 or 4.5, that combines a whole number with a fraction or decimal. Rational numbers encompass all mixed numbers. 315 may be written as 165, making it a logical number. All decimals that either end or start to repeat after a certain point are considered rational numbers. Because 0.2 may be represented as 15, it is a rational number.
Given Data
[tex]\frac{1}{3}[/tex] + 4.1
[tex]\frac{1}{3}[/tex] + [tex]\frac{41}{10}[/tex]
Taking LCM,
[tex]\frac{10+123}{30}[/tex]
[tex]\frac{133}{30}[/tex]
4[tex]\frac{13}{30}[/tex] is the solution of equation as a mixed number in simplest form.
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In 2017, one U.S. dollar was worth 19.61 Mexican pesos. How many dollars was 150.68 pesos worth?
By using unitary method, we get that 150.68 pesos are worth $ 7.6 .
What is unitary method?An individual or singular unit is referred to as unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
We know 1 U.S. dollar = 19.61 Mexican pesos
Thus by unitary method, we get ;
1 Mexican pesos = 1 / 19.61 dollars
this implies 1 Mexican pesos = 0.5099
To find : 150.68 pesos worth
Therefore , 150.68 pesos worth = 150.68 × 0.5099
= 7.683 dollars
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A rectangle has a length of 14 units and a width of 6 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x.
Answer:
f(x) = 4x³ - 40x² + 84x=================================
The box is the right rectangular prism.
Its volume is the product of its three dimensions:
V = lwhWe need to find each dimension and multiply them to get the desired function.
GivenLength = 14 units,Width = 6 units,Cut = x units.SolutionThe height is same as size of the cut, so it is x units.
h = xThe length was 14 units but it is now cut from bot ends so it is now:
l = 14 - 2xThe width was 6 units but it is too cut from the both ends by x units:
w = 6 - 2xWe have all three dimensions, find the volume:
f(x) = x(6 - 2x)(14 - 2x) or, when distributedf(x) = x(6*14 - 6*2x - 2x*14 + 2x*2x) = x(4x² - 40x + 84) = 4x³ - 40x² + 84xV = (14 - 2x) (6 - 2x) x cubic units.
The polynomial function formed by given dats is V=(14 - 2x) (6 - 2x) x
What is polynomial function?A polynomial function is one that involves only non-negative integer powers or only positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, or exponential equation.
Here given,
A rectangle has 14 units of length and 6 units of width.
From each corner of the rectangle, four squares with dimensions of x by x units are cut out.
The box's length is equal to (14 - 2x) units.
The box's width is =(6 - 2x) units.
The box's height is = x unit.
The volume of the box is equal to the sum of its length, width, and height.
Cubic units =(14 - 2x) (6 - 2x) x
∴V=(14 - 2x) (6 - 2x) x
where V is the box's volume in cubic units
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Pic below&;73737 the haheheueu
Answer:
4.)
Radius: 2.4cm
Diameter: 4.8cm
Circumference: 15.072cm
5.)
Radius: 3.5cm
Diameter: 7cm
Circumference: 21.98cm
6.)
Radius: 7cm
Diameter: 14cm
Circumference: 43.96cm
Step-by-step explanation:
Radius: [tex]d[/tex] ÷ [tex]2[/tex]
Circumference: [tex]d[/tex] × [tex]\pi[/tex] or [tex]2[/tex] × [tex]\pi[/tex] × [tex]r[/tex]
Have a great day <3
Energy is measured in kilowatt-hours. The table and scatter plot below, show the cost of building a facility to produce energy and the ongoing cost of operating the facility for five different types of energy.Do you think that there is a statistical relationship between building cost and operating cost? if so, describe the nature of the relationship.
Yes, because it looks like there is a downward pattern in the scatter plot. It appears that the types of energy that have facilities that are more expensive to build are less expensive to operate.
a researcher is conducting an experiment comparing how sleep affects student grades. three different groups are being compared, group 1 sleeps between 2-4 hrs per night, group 2 sleeps between 5-7 hrs per night and group 3 gets over 8 hrs of sleep per night. should the researcher conduct a series of t-tests comparing each group or should one anova be conducted to compare the groups? why?
One ANOVA must be used to compare the groups as there are more than 2 groups and each group has many data values.
The t test, analysis of variance (ANOVA), and covariance analyses are statistical methods used in the testing of the hypothesis for the comparison of means between the groups (ANCOVA).
The Person's t test is used to compare means between two groups, while an ANOVA is used to compare means among three or more groups. In an ANOVA, first is given a shared P value. For at least one pair where the average difference is statistically significant, the ANOVA test yields a significant P value. To identify the crucial pair, we do several comparisons . Two-way ANOVA employs two category independent variables, whereas one-way ANOVA uses simply one categorized independent variable. when there is at least one predictor variableSimilar to other tests, the null hypothesis and the alternative hypothesis are both categories of hypotheses. The alternative hypothesis suggests that there is a statistically significant difference between the means, in contrast to the null hypothesis, which asserts that there is no statistically significant difference in the means.To learn more about ANOVA visit:
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Find the equation of the line that is perpendicular to the line y=x-9
and passes through the point (-7,1)
. Write the equation in point-slope form.
The equation of a line perpendicular to y = x - 9 and passes through (-7, 1) is y = - x - 6
How to find the equation of a line?The equation of a line can be represented in a point slope form as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the coordinatesTherefore, the line is perpendicular to y = x - 9 and passes through (-7, 1).
Perpendicular lines follows the rule:
m₁ m₂ = -1
1m₂ = -1
m₂ = -1
Hence, let's find the y-intercept of the equation of the lines using (-7, 1)
y = - x + b
1 = - (-7) + b
1 = 7 + b
1 - 7 = b
b = -6
Therefore, the equation of the line is y = - x - 6
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Daniyar paid his April FlashCard bill in full. His May bill shows an average daily balance of $270.31 and a monthly periodic rate of 1.65%. What is the finance charge on Daniyar's May statement?
The finance charge would be the amount of $4.46 on Daniyar's May statement.
What is the finance charge?The finance charge is the multiplication of the average daily balance and the monthly periodic rate.
The finance charge = average daily balance × monthly periodic rate
The bill shows an average daily balance of $270.31 and a monthly periodic rate of 1.65%.
The finance charge = $270.31 × 1.65%
The finance charge = $270.31 × 0.0165
Apply the multiplication operation to get,
The finance charge = $4.460115
Round the nearest to the hundredth,
The finance charge = $4.46
Hence, the finance charge would be the amount of $4.46 on Daniyar's May statement.
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Element X decays radioactively with a half life of 13 minutes. If there are 430 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 6 grams?
[tex]y=a(.5)^\frac{t}{h}[/tex]
It will take 80.63 minutes for the element X to decay to 6 grams.
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
Element X decays radioactively with a half life of 13 minutes.
There are 430 grams of Element X.
Since, The half life formula to solve the problem is;
[tex]A = a (0.5)^{\frac{t}{h}[/tex]
Where, A is final amount, a is initial amount, t is time and h is half life.
Now, We have;
A = 6, a = 430, h = 13
Substitute in above equation we get;
[tex]6 = 430 (0.5)^{\frac{t}{13} }[/tex]
Solve for t as;
Divide by 430,
[tex]\frac{6}{430} = (0.5)^{\frac{t}{13} }[/tex]
[tex]\frac{3}{215} = (0.5)^{\frac{t}{13} }[/tex]
Take log both side;
[tex]ln\frac{3}{215} = ln(0.5)^{\frac{t}{13} }[/tex]
[tex]ln 3 - ln 215 =\frac{t}{13} ln(0.5)[/tex]
Substitute values of all the log as;
1.09 - 5.37 = t / 13 (-0.69)
- 4.28 = t/ 13 (-0.69)
13 x 4.28 = 0.69t
55.64 = 0.69t
t = 55.64 / 0.69
t = 80.63
Thus, It will take 80.63 minutes for the element X to decay to 6 grams.
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30+3x=6x
Can someone help me with this pls
Answer: X=10
Step-by-step explanation:
A manager wants to buy headsets for the customer service team members to use. the headsets cost $12 each. the budget allows $155 to be used for customer service equipment, but the manager wants to save more than $20 for later in case it is needed for something else. how many headsets can the manager buy?
Using inequality we can calculate that within the budget the manager can buy 11 headsets.
Any monotonically rising function, as long as both expression portions fall inside the scope of that specific function, can be applied to both sides of an inequality without destroying the relationship between the two.
If a monotonically falling function were applied to both ends of an inequality, the inequality relationship would be inverted.
The equations for the additive reverse and the multiplicative reverse for positive numbers are two examples of employing a monotonically decaying function.
Let the manager can buy x headsets.
Cost of x headsets = 12x
Money saved = 20
Budget = 155
Therefore we write the represented inequality as :
12x + 20 < 155
or, 12 x < 135
or, x < 11.25
Now the number of headsets can not be a decimal number, therefore 11 headsets need to be bought.
Therefore the manager can buy 11 headsets.
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I need help with this
it is upside down sry...
HELP PLEASE
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
Answer:
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
Step-by-step explanation:
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
Write the slope-intercept form of the equation of the line described.
through (2,-4) and is perpendicular to y = 2x +1
The slope-intercept form of the described line's equation. through (2,-4) and is perpendicular to y = 2x +1. y = 2x + 0 is the slope intercept form.
What is slope-intercept form?When you know the slope of the line to be examined and the point given is also the y intercept, We can use the slope intercept formula,y = mx + b. (0, b).
The y value of the y intercept point is represented by b in the formula.Here given a point (2 , -4)
and given an equation, y = 2x + 1
we know that slope intercept form = y = mx + b
to get value of b ,
substitute x and y in perpendicular equation ,
so we get ,
- 4 = 2 x 2 + b
- 4 = 4 + b
- 4 - 4 = b
b = 0;
So the slope intercept form = y = 2x + 0
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