In the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.
What is distributive property?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
So, in this instance, the multiplication is as follows:
5 * 216
This multiplication can be rewritten as follows:
5*(200+16)
We then put the distributive property to use. So, we have:
(5*200) + (5*16)
Therefore, in the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.
Know more about the distributive property here:
https://brainly.com/question/4077386
#SPJ4
Correct question:
Jack broke apart 5x216 as (5x200)+(5x16) to multiply mentally. What strategy did Jack use?
Find the 3 smallest positive x-intercepts of the graph of
y = cos(12x) + cos(16x) and list them in increasing order.
Submit your answer as a list of x-coordinates from least to greatest.
To find the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x), you can use the following steps:
Set y equal to 0 and solve for x to find the x-intercepts of the graph.
Since the graph of y = cos(12x) + cos(16x) is periodic with period 2π/12 = π/6 and 2π/16 = π/8, respectively, you only need to consider x-intercepts in the interval [0,π/6).
Use the identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b) to rewrite the equation y = cos(12x) + cos(16x) as:
y = 2cos(4x)cos(8x) - sin(4x)sin(8x)
Set y equal to 0 and solve for x to find the x-intercepts. This will give you the x-coordinates of all the x-intercepts of the graph.
Sort the x-coordinates in increasing order and take the first three smallest positive values to find the 3 smallest positive x-intercepts.
For example, if you set y equal to 0 and solve for x, you get:
0 = 2cos(4x)cos(8x) - sin(4x)sin(8x)
This equation can be rewritten as:
cos(4x)cos(8x) = sin(4x)sin(8x)
Using the identity cos(a) = sin(π/2 - a) and substituting this into the equation above, we get:
sin(4x)sin(8x) = sin(4x + π/2)sin(8x)
This equation simplifies to:
sin(4x)sin(8x) = sin(4x)cos(8x)
Dividing both sides by sin(4x) and rearranging, we get:
sin(8x) = cos(8x)
This equation holds for all values of x that satisfy sin(8x) = cos(8x), so we can find the x-intercepts by setting these two functions equal to each other and solving for x:
sin(8x) = cos(8x)
sin^2(8x) = cos^2(8x)
sin^2(8x) - cos^2(8x) = 0
1 - cos(16x) = 0
cos(16x) = 1
Thus, the x-intercepts of the graph are at x = 0, x = π/16, x = π/8, x = 3π/16, and so on. Since we are only interested in the 3 smallest positive x-intercepts, we can take the first three values in this list: x = 0, x = π/16, and x = π/8.
Therefore, the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x) are [0, π/16, π/8].
What interest will be earned if $9,000 is invest for 4 years at 12% compounded monthly? Round to 2 decimals.
The required compound interest is $5,510.03
What is compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods.
Given, Principal = $9,000
Time = 4 years
Interest = 12% = 0.12
For compounded monthly, n = 12
The compound amount for monthly compounded is given by
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
or, A = [tex]9000(1 + \frac{0.12}{12} )^{12*4}[/tex]
or, A = 9000[tex](1+0.01)^{48}[/tex]
A = $14510.03
Compound interest = $14510.03 - $9,000 = $5,510.03
Hence, the required compound interest is $5,510.03
To learn more about compound interest
https://brainly.com/question/3989769
#SPJ1
Sam had 1 whole 1/2 m 5/8 m used it for a project. how much rope does San have left.
Sam has 7/8 m of rope left.
What is fraction ?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
To derive a solution, you have to subtract the meter of rope that Sam has from the meter of rope he cut for a project.
Therefore,
1½ - 5/8,
Since the meter of rope Sam had is represent with a mixed fraction, we have to convert it to an improper fraction, and therefore 1½ can also be written as 3/2
Therefore, we have
3/2 – 5/8
To solve this fraction, you need to find the smallest number that can divide the denominator (2 and 8), which is 8.
Now divide the denominators with 8 and multiply the answers you get by the numerators.
Therefore, we have
3/2 -5/8
= 12/8 – 5/8
= 7/8 m.
Therefore, Sam has 7/8 m of rope left.
The smallest number used to divide the denominators is also known as the lowest common denominator (LCD).
A fraction has 2 parts, which are numerator and denominator. The numerator is the number at the top in a fraction while the denominator is the number below in a fraction.
To learn more about fraction from the given link
https://brainly.com/question/78672
#SPJ1
Find each percentage of 75. Explain your reasoning.
1. What is 10% of 75?
2. What is 1% of 75?
3. What is 0.1% of 75?
4. What is 0.5% of 75?
Answer:
1. 7.5
2. 0.75
3. 0.075
4. 0.375
Step-by-step explanation:
Yw, and have a good day to everyone who reads this <3 :)
the triangles are simialr solve for the question mark
you need to show the problem
Maria scored 20 goals in 4 soccer games
last season. Approximately how many
points did Maria average per game?
Answer:
idek
Step-by-step explanation:
x+10=y, then 45 is equal to
plssss help me out thank you if you do
Answer: y = -2x + 5
Step-by-step explanation: I think it's the same one...
Calculate the distance between the points N=(-5, 7) and P=(-1, 3) in the coordinate plane.
Round your answer to the nearest hundredth.
: 0
Distance:
Answer:
distance ≈ 5.66 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = N (- 5, 7 ) and (x₂, y₂ ) = P (- 1, 3 )
d = [tex]\sqrt{(-1-(-5))^2+(3-7)^2}[/tex]
= [tex]\sqrt{(-1+5)^2+(-4)^2}[/tex]
= [tex]\sqrt{4^2+16}[/tex]
= [tex]\sqrt{16+16}[/tex]
= [tex]\sqrt{32}[/tex]
≈ 5.66 units ( to the nearest hundredth )
The sum of two consecutive odd integers is at least 16. Which of the following inequalities would model this statement
The sum of two successive odd integers must be at least 16, hence the inequality will be x+1≥4 and the solution will be x≥3.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Here,
Sum of 2 consecutive odd integer=16
Let them be 2x+1 and 2x+3,
2x+1+2x+3≥16
4x+4≥16
x+1≥4
x≥3
The inequality will be x+1≥4 and solution to the inequality will be x≥3 as sum of two consecutive odd integers is at least 16.
To know more about inequality,
https://brainly.com/question/12679763
#SPJ1
in older adults, a higher level of social support is related to question 20 options: lower levels of physical activity. a higher probability of being institutionalized. an early cognitive decline. a lower probability of depression.
In older adults, a higher level of social support is related to question is D. a lower probability of depression.
What is depression?Depression is a prevalent mental illness. According to estimates, the disorder affects 5% of adults worldwide. Consistent sadness and a lack of interest in previously fulfilling or enjoyable activities are its defining traits. Additionally, it may impair appetite and sleep. Concentration problems and fatigue are frequent.
A severe mental illness called major depressive disorder has an impact on how people feel, think, and carry out their daily activities. The condition may also affect a person's ability to enjoy life, appetite, and sleep patterns. When there's social support, people are happier and this reduce depression.
Learn more about depression on:
https://brainly.com/question/21711771
#SPJ1
You are preparing to purchase some items online. You have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items. Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy. In terms of this scenario, what does the point (9 , 1) mean?
, You are preparing to purchase some items online. You have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items. Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy. In terms of this scenario, what does the point (9 , 1) mean?
The point (9 , 1) means you cannot buy 10 items total.
The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes.
The point (9 , 1) means you can buy 9 pairs of shoes and 1 pair of jeans.
The point (9 , 1) means you cannot buy 9 pairs of shoes and 1 pair of jeans.
In terms of this scenario, the point (9 , 1) means B. The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, you have a total of $320 to spend. You see several styles of shoes you like and each pair costs $16. You also like several pairs of jeans and each pair costs $32. You want to purchase more than 6 items.
Let x represent the number of pairs of shoes you can buy, and y represent the number of pairs of jeans you can buy.
The point (9 , 1) means you can buy 9 pairs of jeans and 1 pair of shoes. This can be illustrated as:
9($32) + 1($16)
= $282 + $16
= $298
The correct option is B.
Learn more about equations on:
https://brainly.com/question/2972832
#SPJ1
What types of values of the test statistic for the kruskal wallace test support the alternative hypothesis?.
Answer:
that at least one of the distributions function is not equal.The area of a rectangle is 2 square feet. The perimeter of the rectangle is 9 ft. Find the length, ll, and width, ww, of the rectangle. What is l^2 + w^2l 2 +w 2 ?.
The rectangle is 4 feet long and 0.5 feet wide. l²+w² equals 16.25 feet².
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area is a phrase used to describe how much room a 2D form or surface occupies.
Here,
Let l be the length and w be the width.
area=2
lw=2
w=2/l
2(l+w)=9
2l+2w=9
2l+2*2/l=9
2l²+4=9l
2l²-9l+4=0
l=0.5,4
w=4,0.5
l=4 and w=0.5
l²+w²=4²+0.5²
=16.25 feet²
The length of rectangle is 4 feet and width is 0.5 feet. The value of l²+w² is 16.25 feet².
To know more about area,
https://brainly.com/question/13194650
#SPJ4
calculate the diameter of a circle with an area of 56
Answer:8.44
Step-by-step explanation:
Area of the circle is 56.
Divide 56 by 3.14(Pi)
56/3.14=17.8343949
Square root it
Square root of 17.8343949=4.223078841
4.22 is the radius so to find the diameter you just multiple by 2.
4.223078841x2=8.446157683
Peter and John are running around the town around the town in opposite directions. Peter can go around the town in 2.5 hours, and John can do the same in 15 hours. Assuming they start at the same time and same place, how many times will they pass each other going in opposite directions in a 24-hour period?
Answer:
90
I am not too sure but this question is VERY BRAIN-INTENSIVE
Sorry, if i am wrong
Determine the equation of the parabola that opens up, has vertex (-4,-8)(−4,−8), and a focal diameter of 1616.
The equation of parabola will be;
⇒ y = 4 ( x + 4)² - 8
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The vertex = (- 4, - 8)
And, The focal diameter = 16
Now,
Since, The vertex (h, k) = (- 4, - 8)
And, The focal diameter (4a) = 16
⇒ 4a = 16
⇒ a = 4
Hence, The equation of parabola with vertex (h, k) will be;
⇒ y = a (x - h)² + k
Substitute all the values, we get;
⇒ y = 4 (x - (-4))² + (-8)
⇒ y = 4 ( x + 4)² - 8
Thus, The equation of parabola will be;
⇒ y = 4 ( x + 4)² - 8
Learn more about the parabola visit:
https://brainly.com/question/11844921
#SPJ1
a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?
If the expected value of d is not equal to d, then the property that d hat exhibit is option (E) d hat is biased
Here a certain statistic d cap is being used to estimate a population parameter d
The central limit theorem states that "the distribution of sample means approximates a normal distribution as the sample size gets larger."
According to the central limit theorem,
The expected value is μ = p
Then the standard error will be
s = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
Here it is given that the expected value of d cap is not equal to d. So it is different from the expected value μ = p.
Therefore, the d hat is biased
I have answered the question in general, as the given question is incomplete
The complete question is :
A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?
A. The sampling distribution of d hat is normal.
B. The sampling distribution of d hat is binomial.
C. The sampling distribution of d hat is uniform.
D. d hat is unbiased.
E. d hat is biased.
Learn more about central limit theorem here
brainly.com/question/18403552
#SPJ4
Translate this phrase into an algebraic expression.
60 decreased by twice Jenny's score
Use the variable to represent Jenny's score. please help.
The expression for 60 decreased by twice Jenny's score 60 - 2x.
What is an algebraic expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Let Jenny's score be x.
Twice Jenny's score will be 2x.
Therefore, the expression will be:
= 60 - 2x
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. what is the maximum possible weig...
In linear equation, 3 t is the maximum possible weight .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Assuming x to be lightest , y median and z the heaviest.
So according to given information average is 7 so total sum for three box = 21
thus x+y+z = 21
Given y=9 (median weight)
thus x+z = 12
For maximum possible value for x is 3 such that z= 9
if x=4 then Z= 8(this changes median to 8)
So maximum possible value for lightest box is 3
Learn more about linear equation
brainly.com/question/11897796
#SPJ4
Cameron has papayas and bananas in a ratio of 6:19. How many bananas does he have if he has 36 papayas?
Answer: 113 bananas
Step-by-step explanation:
The ratio is 6:19, with 6 papayas for every 19 bananas.
We have 36 papayas, which is 6 times, so we just need to get 19 times 6 = 113 bananas
what is the distance between -5, -3 and -5, -6
To calculate the distance between the points -5, -3 and -5, -6. We apply the following formula:
(x₁, y₁) and (x₂, y₂) d = √(x₂ - x₁)² + (y₂ - y₁)²
The points are:
(x₁ = -5, y₁ = -3) and (x₂= -5, y₂= -6)
We apply the above formula and solve.
d = √(x₂ - x₁)² + (y₂ - y₁)²d = √ (-5 - (-5))² + (-6 - (-3))²d = √ 02 + (-3)² = √ 0 + 9d = √9 = 3The distance between the points -5, -3 and -5, -6 is 3.
please help me solve this: solve for x
Answer:
x = 100
Step-by-step explanation:
You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.
Richard and Teo have a combined age of 32. Richard is 8 years older than twice Teo's age. How old are Richard and Teo?
Answer: Richard =24 Teo = 8
Step-by-step explanation:
32-8 = 24
24-8 = 16
16/2= 8
A. How many cube with an edge length of b. What i the volume, in cubic inche, of inch are needed to build a cube with one cube with an edge length of inch? an edge length of 1 inch?
In order to build a cube with an edge length of b inches, b3 cubes with 1-inch edges are required.
What are cubes?A cube is a three-dimensional object with six square faces that are all the same size and form in mathematics. A cube has perpendicular sides and is symmetrical along all three axes. Finding the area of one of a cube's faces and increasing it to the third power yields the volume of the object. V=s3, where s denotes one of the cube's sides, is the formula for calculating a cube's volume. Cubes are frequently used in geometry and algebra, and they have a wide range of real-world uses, including volume measurement and the solution of mathematical equations.
How to solve?
The volume of a cube with an edge length of b inches is b3 cubic inches. For instance, if b=3, we would require 33=27 cubes with 1 inch-long edges, and the volume of a cube with a three inches edge would be 33=27 cubic inches.
To learn more about cubes, visit:
https://brainly.com/question/28134860
#SPJ4
Name the vertices of the following points when they have been translated 6 units to the right and 10 units up A(1,-1) B (2, -2) C(-2,2)
A. C’(8,8)
B. C’(-8,-8)
C. C’(4,12)
D. C’(-4,12)
The translated points are A'(7, 9), B'(8, 8), and C'(4, 12) when they have been translated 6 units to the right and 10 units up.
What is a coordinate plane ?A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.
The given points are,
A(1, -1), B (2, -2) and C(-2, 2).
When the points are translated 6 units to the right and 10 units up implies that,
There will be increase of 6 units in x coordinate and increase of 10 units in y coordinate
The point coverts as
A'(7, 9), B'(8, 8), and C'(4, 12)
The translated points are A'(7, 9), B'(8, 8), and C'(4, 12).
To know more about Coordinate plane on:
https://brainly.com/question/24134413
#SPJ1
Denise earns $225 a week with a part time job at the local florist. She decides to put 30% of the amount into a saving account. How much money does Denise put in the savings account each week?
Denise puts $67.50 in the savings account every week.
What is a percentage?
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.
To find out how much money Denise puts in the savings account each week, you need to multiply her weekly earnings by the percentage she puts into the savings account.
First, convert the percentage to a decimal by dividing by 100: 30% = 0.30
Then, multiply Denise's weekly earnings by this decimal to find the amount she puts into the savings account each week:
=$225 * 0.30
=67.50.
Hence, Denise puts $67.50 in the savings account each week.
To learn more about the percentages, visit:
https://brainly.com/question/24877689
#SPJ1
3. Write an equation that represents the line that passes through the point (7,4) and has a slope of 4/9
A company has 30 employees 20 female 10 male, the board of directors decides to ask a group of 10 people, half of which are male, about expanding the company. Determine how many possible groups are there?
Answer:
M=960
F=480
Step-by-step explanation:
look at the work I did
Geometry: Which chord is nearest the center and why? (ASAP!!!)
Chord AC is the nearest to the center because the perpendicular distance of chord AC from center O is the smallest.
What is a chord of a circle?
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line or just secant. More generally, a chord is a line segment joining two points on any curve, for instance, an ellipse.
ΔABC is inscribed in O. If AB = 5, BC = 8, and AC =9.
Now if you look carefully at the given diagram, we can see that the perpendicular distance of chord AC from center O will be smaller than the perpendicular distance of chord AB from center O and the perpendicular distance of chord BC from center O.
Hence, Chord AC is the nearest to the center because the perpendicular distance of chord AC from center O is the smallest.
To learn more about the chord of a circle, visit:
https://brainly.com/question/1869643
#SPJ1