Answer:
To find the GCF of 2^5·5·11 and 2^3·5^2·7, we first prime factorize each number:
2^5·5·11 = 2^5 x 5 x 11
2^3·5^2·7 = 2^3 x 5^2 x 7
Next, we look for the highest power of each prime factor that they both have in common:
2^3 is the highest power of 2 that both numbers have.
5^2 is the highest power of 5 that both numbers have.
So, the GCF of 2^5·5·11 and 2^3·5^2·7 is 2^3 x 5^2 = 180.
Step-by-step explanation:
A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as
much in the lower-yielding account because it is less risky. His annual interest is $3982 dollars. How much did he invest at
each date?
Your answer is:
Amount invested at 6% equals $
Amount invested at 10% equals
The amount invested in savings with annual interest rate of 6% and 10% is $398200 and $199100.
What is simple interest?Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Let S be his savings.
He divided S into x that goes at 6% and y at 10%
As he put twice as much at the lower-yielding one, x = 2y.....(1)
Simple interest is given by: Amount x interest x time
Thus,
SI₁ = x . 0.06 . 1 = 0.06x
S I₂ = y. 0.10 . 1 = 0.10y
As x = 2y, I₁ = = 0.06 . 2y = 0.12y
As we know that the annual interest was $3982
SI₁ + SI₂ = 3982
0.12y + 0.10y = 3982
0.22y = 3982
y = 3982/0.22
y = 18100
As x = 2y, x = 36200
Hence, the amount invested is $36200 and $18100.
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Please show all work n tyy :))
The Angle C is 83.2°
Describe Law of Cosines?The Law of Cosines, also known as the Cosine Formula, is a mathematical relationship that relates the lengths of the sides of a triangle to the cosine of one of its angles. The law states that in a triangle ABC with sides a, b, and c opposite to angles A, B, and C, respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab cos(C)
where "cos" represents the cosine function. The Law of Cosines can be used to find missing sides or angles in a triangle when given sufficient information. It is widely used in geometry, trigonometry, and engineering. The Law of Cosines is an extension of the Pythagorean theorem and can be used when the triangle is not a right triangle. It is a powerful tool for solving a variety of problems in a wide range of fields.
To find the angle C in triangle ABC, you can use the Law of Cosines. The Law of Cosines states that in a triangle ABC with sides a, b, and c and opposite angles A, B, and C, the following equation holds:
c² = a² + b² - 2abcos(C)
In this case, a = 20 cm, b = 29 cm, and c = 24 cm, and we are given that angle BAC = 82 degrees. Using this information, we can calculate cos(C) as follows:
cos(C) = (a² + b² - c²)/(2ab) = (20² + 29² - 24²)/(2×20×29) = 0.2618
Finally, we can use the inverse cosine function (arccos) to find angle C:
C = arccos(cos(C)) = arccos(0.2618) = 83.2 degrees (rounded to one decimal place).
So, angle C in triangle ABC is approximately 83.2 degrees.
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Cannot figure out how to answer this question
The correct statement regarding the continuity of the function is given as follows:
All three conditions for continuity are true, so f(x) is continuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For this problem, we must look at the turning point at x = 3, hence:
The lateral limits are equal, as the graph approaches x = 3 by the left and by the right of x = 3 at the same point.f(a) = f(3), due to the closed interval on the graph.Hence all conditions are satisfied and the correct option is given by the fourth option.
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The ten numbers from 1 to 10 are split into two groups. The sum of the numbers in one group is n, and the product of the numbers in the other group is n. What is the largest possible value of n?
I got the answer,( thx to the person who helped me) but I need help with the ratio table and the ordered pairs.
The required cost of the construction of a 4.5-inch tower is $114.75.
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, and thereafter solving those equations. and a single variable.
The parameters given are;
The cost of construction = $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 * 4.5
= $114.75.
We conclude that, the figure above is the amount to fund 4.6 inhces
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Complete question is;
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?
12
Erin
Enn (EDUID: 517931638) 10-2525-19
Calculator Line Rea
....
An average ant can lift a maximum of 50 times its own body weight.
An average ant weighs 4 milligrams.
An average human being weighs 80 kilograms.
Enter the maximum amount of weight, in kilograms, a human being could lift if it could lift as much as an average
ant.
The maximum amount of weight, a human being could lift is 0.0002 kilograms.
How to determine the maximum amount of weightSince an average ant can lift a maximum of 50 times its own body weight, and it weighs 4 milligrams,
The maximum weight it can lift is
50 * 4 milligrams = 200 milligrams.
To convert milligrams to kilograms, we divide by 10^6:
200 milligrams / 10^6 = 0.0002 kilograms
So, the maximum amount of weight a human being could lift if it could lift as much as an average ant is 0.0002 kilograms.
Therefore, the answer is 0.0002 kilograms or 0.2 grams
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Before refrigerators existed some people have blocks of ice delivered to their homes that delivery wagon had a storage box in the shape of a rectangular prism that was 7 1/2‘ x 6‘ x 6‘ the cubic ice blocks stored in the box head slight side lengths, one and a half feet how many ice blocks fit in the storage box
The required number of ice blocks that fit in the storage box is 80 ice blocks.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
The volume of the storage box is,
= 7.5 feet × 6 feet × 6 feet
= 270 cubic feet.
Each ice block has a volume,
= 1.5 feet × 1.5 feet × 1.5 feet
= 3.375 cubic feet.
Therefore, the number of ice blocks that fit in the storage box is,
= 270 / 3.375
= 80 ice blocks.
Thus, the required number of ice blocks that fit in the storage box is 80 ice blocks.
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Draw a model and solve 3*5/6
Answer: 2 1/2 or 2.5
Step-by-step explanation: 3/1 * 5/6= 15/6
divide 15/6 which equals 2.5 or 2 1/2
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
(x - 6)² + y² = 36 and x2 + (y + 6)2 = 36.
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)² + (y - k)² = r².
So, for a circle with a diameter of 12 units, the radius is 6 units.
For the center of the circle to lie on the y-axis, the x-coordinate, h, is 0.
So, the equation for a circle with center (0, k) and radius 6 units is:
(x - 0)² + (y - k)² = 6²
x² + (y - k)² = 36
Two possible values for the y-coordinate of the center, k, that would give us two different circles are k = 6 and k = -6.
So, the two equations are:
x² + (y - 6)² = 36
and
x² + (y + 6)² = 36.
Use the number line below to determine which of the following answer choices had statements that are all true
The choice that had statements that are all true is (a) Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2
How to determine the choices that had statements that are all trueThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The number line
On the number line, we have the following
A = -4
B = -2 1/2
C = 1
D = 1 3/4
When the above values are compared with the list of options, we have
Option (A) = true
This is so because in (a)
Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2
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PLS ANSWER QUICK CORRECTLY!!!! help ya girl ouu!
what is the period of the sinusoidal function? enter your answer in the box.
The period of the sinusoidal function in this problem is given as follows:
10 units.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating in intervals over the domain.
Then the period of the function is defined as the difference between two points in which the function has the same behavior.
For this problem, the function has the same behavior at x = 8 and at x = -2, hence the period of the sinusoidal function is calculated as follows:
Period = 8 - (-2)
Period = 8 + 2
Period = 10 units.
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Determine all numbers at which the function is continuous.
Answer:
(-infinity,-1)U(-1,infinity)
Step-by-step explanation:
plug in the number where the piecewise function changes which is -1 and 1
(-1)^2-(-1)-2 =0
(-1)=-1
These aren't equal so the function is discontinuous at x = -1 because of a jump
(1) = 1
-2(1) + 3 = 1
These are equal so the function is continuous at x = 1
So from negative infinity to -1 the function is continuous and from -1 to infinity
(-infinity,-1)U(-1,infinity)
Please help been stuck on this for hours
The size of angle ACB to the nearest degree is 88 degree.
How is a triangle ABC put together?
Construction Steps:
Create a line segment BC with the property AC = 4 cm.
Draw two arcs that meet at point A by using B as the centre and a radius of 4 cm, and C as the centre and a radius of 7 cm.
Join AB and AC now. Consequently, the necessary triangle is ABC.
With the use of a compass, draw a line segment AB = 7 cm from A, cutting an arc AC = 4 cm.
Cut an arc of 3 cm from point B.
Embrace BC and AC
Triangle with angle ABC is necessary.
< ACB = 88 degree
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18. Casey wants to start a garden.
A) If Casey buys 9 plants
how much was spent on
gardening supplies?
100
Total
cost of 80
garden 60
supplies
(S)
40
20
B) How many plants can
Casey get if her total budget
is $60 for gardening supplies?
C) What is the rate of change?
H
3 6 9 12
9 12 15
Number of plants bought
20
B) What c
3 Bed
C) Is the
20. Bria
and serv
beef is p
table.
BARB
Numb
a) The amount of the supplies is $70
b) The number of the plants is 3
c) The rate of change is 1/20.
What is a proportional relationship?
A proportional relationship is a mathematical relationship between two variables where their ratio is constant. In other words, as one variable increases or decreases, the other variable also increases or decreases in the same ratio.
We have to note that we can read up the relationship from the graph. The amount of the supplies for 9 plants is $70. If the total budget is $60 then we can only have three plants. The rate of change is therefore 1/20.
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David has two part time jobs. He earns $14/h at one and $11/h at the other. David wants to know how many hours it will take him to earn $1000. Find the combinations of the numbers of hours David could work at each job to earn $1000
Answer:
Step-by-step explanation:
To find the number of hours David has to work at each job, we can set up an equation. Let's say David works x hours at the first job and y hours at the second job. Then, we have:
14x + 11y = 1000
Next, we need to find the possible combinations of x and y that satisfy this equation. To do this, we can use trial and error, or use the substitution method. Let's use the latter method. Solve for x in terms of y:
14x = 1000 - 11y
x = (1000 - 11y) / 14
Now, we can substitute this expression for x into the original equation to get a new equation in terms of y:
11y = 1000 - 14x
y = (1000 - 14x) / 11
We can use this equation to find possible values of y. For example, if x = 40 hours, then y = (1000 - 14 * 40) / 11 = (1000 - 560) / 11 = (440) / 11 = 40. So, David could work 40 hours at the first job and 40 hours at the second job to earn $1000.
We can repeat this process for other values of x to find more combinations. Some possible combinations of the numbers of hours David could work at each job to earn $1000 are:
40 hours at the first job and 40 hours at the second job
45 hours at the first job and 35 hours at the second job
50 hours at the first job and 30 hours at the second job
55 hours at the first job and 25 hours at the second job
60 hours at the first job and 20 hours at the second job, etc.
DIG DEEPER In each level of a video
game, you can earn up to 10 points
and lose up to 3 points. Your friend
earns 9 points in the first level. If he
earns and loses the maximum number
of points each level, how many total
points will he have after level 6?
Answer:51
Step-by-step explanation:
9+7+7+7+7+7+7
(or 9+7^6)
As dry air moves upward, it expands and cools. Suppose that the ground temperature is 20°C and
the temperature at a height of 1 km is 10°C.
Input Variable: Height (h), Output Variable: Temperature (T)
Axes: h (km) | 0 | 1 , T (°C) | 10 | 10
Slope: 0 (The temperature does not change with increasing height)
What is ideal gas law?The theory used in this question is the ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are directly proportional.
As the dry air moves upward, it expands and the temperature decreases. This is why the temperature at a height of 1 km is 10°C.
Determine the input and output variables:
The input variable is the height (h) and the output variable is the temperature (T).
Draw and label two axes: On the x-axis, label it "h (km)" and on the y-axis, label it "T (°C)".
Plot and label the two points you were given:
Plot a point at (0, 10) and another point at (1, 10).
Determine the slope of the line between your two points:
The slope of the line between the two points is 0, indicating that the temperature does not change with increasing height.
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You are planning your brother's mini surprise party, and you want to take
him and his closest friends to a sporting event. His two favorite sports are
hockey and basketball. Each local team offers a special party suite during
the game. The hockey suite costs $130 to rent the room and $30 per
person. The basketball suit costs $180 to rent the room and $20 per
person. Identify the system of equations that represents this model, where
y represents the total cost of the party, and x represents the number of
people attending the party.
The system of equations that models the situation is given as follows:
y = 130 + 30x.y = 180 + 20x.How to construct the system of equations?The system of equations is constructed by linear functions in slope-intercept format, which are explained as follows:
y = mx + b.
In which:
The slope m represents the variable cost, that is, the cost per player.The intercept b represents the fixed cost, that is, the cost per room.Hence the two functions are given as follows:
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Find the measure of the three missing angles in the rhombus below.
Answer:
see below
Step-by-step explanation:
Remember this definition:
A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.
so if you know only 1 angle, you'll know all of them
because z is opposite to the given angle 69 so z=69
the other 2 angles are the same = 180 -69 =111
NEED ANSWER ASAP!!
How much water should be added to 18 mL of 15% alcohol solution to reduce the concentration to 9%?
What function is graphed below?
y=x/3-1
y=3x
y=x-3
y=x+3
Answer:
(a) y = x/3 -1
Step-by-step explanation:
You want the equation of the line graphed showing points (3, 0) and (6, 1).
SlopeThe slope of the line is its "rise" divided by its "run." Here, the points are 3 units apart horizontally, and 1 unit vertically, with the line going up to the right. That means ...
slope = rise/run = +1/+3 = 1/3
Slope-intercept equationThe slope-intercept form of the equation for a line is ...
y = mx +b . . . . line with slope m and y-intercept b
The slope of 1/3 means the coefficient of x will be 1/3. There is only one answer choice like that:
y = x/3 -1
Find the range, interquartile range, quartile deviation, mean absolute
deviation, population variance, and population standard deviation of
the given ungrouped data.
There are 12 sections of Statistics 1 in a state university. Listed below
are the number of students enrolled in each section.
23 43 56 43 23 56 43 23 15 14 38 44
The required range of the given data set is 42 and defined for the interval (14, 56).
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Range: The range is the difference between the largest and smallest values in a set of data.
Here,
The largest value is 56 and the smallest is 14, so the range is given as,
= 56 - 14 = 42.
Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
Quartile deviation (QD): The QD is also known as the semi-interquartile range, and is half the interquartile range (IQR).
Mean Absolute Deviation (MAD): The MAD is a measure of variability that is calculated by finding the average of the absolute deviations of each data point from the mean.
Population Variance: The population variance is a measure of how much the data points in a population deviate from the mean.
Population Standard Deviation: The population standard deviation is the square root of the population variance, and is a measure of how spread out the data points in a population are.
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Note: The calculation of IQR, QD, MAD, population variance, and population standard deviation would require more steps, but these calculations are beyond the scope of this answer.
How many ways can you scramble the word “Oaxaca”
Answer:
oaxaca
oacaxa
xaoaca
xacaoa
caoaxa
caxaoa
aoaxac
axaoac
aoacax
acaoax
axacao
acaxao
aoxaca
aocaxa
acoaxa
acxaoa
axoaca
axcaoa
aoaxca
axaoca
aoacxa
axacoa
acaoxa
acaxoa
Looks like 24 to me.
6 arrangements of “oa” “xa” and “ca”
those same 6 reversed
those same 6 with the first pair reversed
those same 6 with the first two pairs reversed.
reversing the last pair or the last two pairs only is illegal, so this is comprehensive.
Step-by-step explanation:
HELP
______________________________
The graph of the function is given by the image presented at the end of the answer.
The minimum value on the interval [-2,0] is given as follows:
y = -1 at x = -2.
The maximum value on the interval [-2,0] is given as follows:
y = 1 at x = 1.
How to obtain the minimum and the maximum values of a function?The minimum value of a function in an interval is the lowest value of y assumed by the function.
The maximum value of a function in an interval is the lowest value of y assumed by the function.
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Last season, a sports fan spent $3,232 to see her favorite team play 32 games. To see each game, the fan had to buy a ticket and pay $25 for parking. Let p represent the amount the fan paid for each ticket. Write an equation that represents the total amount the fan paid. A friend of the sports fan bought 9 tickets at the same price. How much did the friend spend?
The equation that represents the total amount the fan paid is
32 x (P + 25) = 3,232.
The amount spent by the friend is $909.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
Amount spend for 32 tickets = $3,232
Cost of parking = $25
Let p represent the amount the fan paid for each ticket.
The cost of each ticket.
32 x (P + 25) = 3,232
Solve for P.
32 x (P + 25) = 3,232
P + 25 = 3,232/32
P = 101 - 25
P = $76
Now,
The amount spent by the friend.
= 9 x (76 + 25)
= 9 x 101
= $909
Thus,
32 x (P + 25) = 3,232 represents the total amount the fan paid is
The amount spent by the friend is $909.
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Y varies directly as X and Y=39 when X = 52 find Y when X = 22
35?
I just subtracted 39 from 52 and i got 14 so i added 13 to 22 and i got 35 so i assume thats it
a realtor earns 1.25 % commision on the price of any home that she sells last month she sold two homes for A total homes for a total of $750,000 how much money in commisions did the reaitor earn
The total commission the realtor earns is given by the equation A = $ 9375
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total commission amount the realtor earns be represented as A
Now , the equation will be
The percentage of commission = 1.25 %
The total amount for the 2 homes = $ 750,000
So , the amount of commission A = percentage of commission x total amount for the 2 homes
Substituting the values in the equation , we get
The amount of commission A = ( 1.25 / 100 ) x 750,000
On simplifying the equation , we get
The amount of commission A = 0.0125 x 750,000
The amount of commission A = $ 9375
Hence , the amount of commission is $ 9375
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Three large cones hang from the ceiling in an office building in front of a bank of windows. The height of each cone is 12 feet and the circumference of the base of each cone is 8π feet. The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black. What is the total surface area painted black? Use π≈3.14. Enter your answer, rounded to the nearest tenth, in the box.
The total surface area painted black = 90.5 square feet to the nearest tenth.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.
Given:
Three large cones hang from the ceiling in an office building in front of a bank of windows.
The height of each cone is 12 feet, and the circumference of the base of each cone is 8π feet.
The base and 40% of the lateral surface of each cone is painted red, and the rest of each cone is painted black.
Circumference of the base of the cone = 8π feet.
2πr = 8π
πr = 4π
The surface area of the cone = πr x height
The surface area of the cone = 12 x 4π
The surface area of the cone = 48π.
The total surface area painted black = 60% of 48π.
The total surface area painted black = 90.5 square feet to the nearest tenth.
Therefore, the result is 90.5 square feet to the nearest tenth.
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The sum of two numbers is a 16. The product is 64. Name the numbers?
Answer: [tex]8[/tex] and [tex]8[/tex]
Step-by-step explanation:
Let the numbers be [tex]x[/tex] and [tex]y[/tex].
[tex]x+y=16 \implies y=16-x\\\\xy=64 \longrightarrow x(16-x)=64\\\\16x-x^2 =64\\\\x^2 -16x+64=0\\\\(x-8)^2=0\\\\x=8 \implies y=8[/tex]
4. The density and strength of concrete are determined by the ratio of cement and aggregate. Suppose that a contractor has 450 cubic feet of a dry concrete mixture that is 60 % sand by volume. How much pure sand must be added to form a new mixture that is 80% sand by volume?
The amount of sand that must be added to form a new mixture that is 80% sand by volume will be 90 cubic feet.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The thickness and strength of not entirely set in stone by the proportion of concrete and total. Assume that a project worker has 450 cubic feet of a dry substantial blend that is 60 % sand by volume.
The amount of sand that must be added to form a new mixture that is 80% sand by volume is given as,
⇒ 0.80 x 450 - 0.60 x 450
⇒ 360 - 270
⇒ 90 cubic feet
The amount of sand that must be added to form a new mixture that is 80% sand by volume will be 90 cubic feet.
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