The number of positive integers smaller than 1000 that are divisible by 7 must be determined using the rule of arithmetic progression.
There are 142 positive integers that are divisible by 7 that are less than 1000.
The positive numbers below 1000 that can be divided by seven include
7, 14, 21, 28,..........994.
The final number under 1000 that is divisible by 7 is 994.
An arithmetic progression's common form is [tex]T_{n} = a + (n-1)d[/tex]
where d is the common difference, n is the number of terms, and a is the first term.
We've :
a is 7 and d is 7.
When we generalize these values, we get at:
[tex]T_{n} = a + (n-1)d\\994 = 7 + (n-1)7\\994 -7 = 7n - 7\\994 = 7n \\n =\frac{994}{7} =142[/tex]
There are hence 142 positive integers below 1000 that are divisible by 7.
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1. The distance between two cities on the map was 6.5 cm. If the scale of the picture is 1:5000000, find the distance between the two cities.
2. How many centimeters can be used to represent a distance of 650 km on a map with a scale of 1:1500000?
3. If the distance between Ulaanbaatar and Choibalsan is 630 km, and the distance between these cities is shown on the map as 7 cm, find the scale of the map.
Considering the given scale, it is found that:
1. The distance between the two cities is of 325 km.
2. 43.3 cm should be used to represent the distance.
3. The scale of the map is of 1:9000000.
What is a scale?A scale is how much each unit in the drawing represents in actual distance.
For item 1, the scale of 1:5000000 means that each unit on the graph represents 5,000,000 units of actual distance.
The distance on the map is of 6.5 cm, hence the actual distance is of:
6.5 x 5000000 = 32,500,000 cm = 325 km.
For item 2, the scale is of 1:1500000, meaning that each cm of drawing is equivalent to 1,500,000 cm of real distance = 15 km.
Hence, the number of centimeters to represent a distance of 650 km is given by:
650/15 = 43.3 cm.
For item 3, we have that 7 cm represent 630 km = 63,000,000 cm, hence:
63,000,000/7 = 9000000.
Meaning that the scale is given by:
1:9000000.
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Please help me fast I will mark brainliast
Answer:
See attached worksheet.
Step-by-step explanation:
machine A creates 6 products in 20 minutes .machine B can create the same products at a rate of 1 product per 4 minutes which machine works faster
Answer: Machine A is faster
Step-by-step explanation:
1) Make them into fractions.
Machine A: 6/20
Machine B: 1/4
2) Make the denominator the same
Machine A: 6/20
Machine B: 1/4 * 5/5
Machine A: 6/20
Machine B: 5/20
6/20 > 5/20
Machine A > Machine B
help please please help thanks
A monopoly player claims that the probability of getting a when rolling a six-sided die is because the die is equally likely to land on any of the six sides. Is this an example of a theoretical probability or an empirical probability? explain.
It is an illustration of theoretical probability.
Theoretical probability establishes the probability of certain events occurring.
The ratio of the entire number of conceivable possibilities to the intended outcome is known as theoretical probability.
In this case, the intended consequence is earning a 2, which is only one of the six potential possibilities. The possibility of receiving a 2 is.
Observance determines empirical probability. Nothing about the observing of the specified episode is indicated in the question, hence it is not an empirical probability.
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At class meeting, Jeff, Chad, and Lane ate a total of 254 marshmallows in the marshmallow-eating contest. Jeff won by eating 7 more marshmallows than Chad, who ate 5 more than Lane. How many marshmallows did Jeff eat?
The equation is formed and solved below.
What is an equation?
A mathematical equation is a calculation that uses the matching sign to represent the similarity of two expressions. A polynomial equation is the most prevalent kind of equation. An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance.
Lane ate = x marshmallows (let)
Chad ate = x + 5 marshmallows
Jeff ate = (x + 5) + 7 = x + 12 marshmallows
Then, the equation formed is
x + x + 5 + x + 12 = 254
The equation is solved as
3x + 17 = 254
or, 3x = 254 - 17
or, x = 237/3 = 79
Jeff ate = 79 + 12 = 91 marshmallows
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15. pls help need to turn in asap by midnight
The equation of a line in the point-slope form will be:
(y2 - y1) = m (x2 - x1)
As per the table, the equation of this line in the point-slope form will be:
(30 - 25) = m (130-120)
Now,
(30 - 25) = m (130-120)
⇒ 5 = m (10)
⇒ m = 10/5 = 2
So, the slope of this line = m = 2
In the Slope - Intercept form, the equation is written as:
y = mx + c
⇒ y = 2x + c
The value of c = 0.
What is the Slope of a line?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. A common symbol for slope is the letter m. Finding the ratio of "vertical change" to "horizontal change" between any two distinct points on a line yields the slope. The ratio can also be written as a quotient, which produces the same number for every two different points on the same line. A negative "rise" refers to a decreasing line. The line could be functional, set by a road surveyor, or depicted in a diagram that represents a road or a roof as a description or a plan.The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn in one of four directions: upward, downward, horizontal, or vertical.To learn more about the Slope of a line, refer to:
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Answer the following
Answer:
Don't know
Step-by-step explanation:
plsss help i just need help on how to do it i’ll give brainliest
The expression that represents the perimeter of the other shape is 9x + 6y.
Option(b) is the correct one.
What is an Expression in Math?Expressions in mathematics are mathematical statements that comprise at least two terms that contain numbers, variables, or both, and are joined by an operator. Addition, subtraction, multiplication, and division are all examples of mathematical operators.
Given:
Expression for the sum of the perimeter of two shapes = 13x + 4y
Expression for the perimeter of one shape = 4x - 2y
Expression for the perimeter of the other shape is,
(13x + 4y) - (4x - 2y)
= 13x - 4x + 4y + 2y (combine the like terms and solve)
= 9x + 6y
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a bank sends its customers an e-mail when their accounts fall below -10$. Which inequality models this situation??
The inequality which models the given situation will be;
⇒ x < - $10
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The condition is;
''A bank sends an e-mail to its customers when their accounts fall below -10$.
Now,
Let the total balance in his account = x
Then, we can formulate;
The inequality for the given situation is;
⇒ x < - $10
Therefore,
The inequality which models the given situation will be;
⇒ x < - $10
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One side of an envelope is 3 inches longer than the other side. The area of the envelope is 108 in²Determine the dimensions of the envelope.
Dimensions of envelope will be Length will be (x + 3) = (9 + 3) = 12 and Breadth will be x = 9.
Envelope can be considered as the shape of rectangle.
Rectangle has length and breath which can be considered as the sides of envelope.
Now we have given one side of envelope is 3 inches longer than the other side of envelope.
let side of envelop be x inches than other side will be (x + 3) inches.
Now we have also given that the area of envelop is 108 in².
The Area of rectangle = (length)(breadth).
let length of envelop be (x+3) as its bigger than its breadth x.
∴ Substitute area of rectangle with the area of envelope.
∴ (x + 3)(x) = 108.
∴ x² + 3x = 108.
∴ x² + 3x - 108 = 0.
∴ x² + 12x -9x - 108 = 0
∴ x(x + 12) -9(x +12) = 0
∴ (x-9) (x +12) = 0
∴ (x-9) = 0 and (x +12) = 0
∴ x = 9 and x = -12
Now as dimensions cannot be negative ∴ x = -12 is rejected.
∴ x = 9 is considered
∴ Length will be (x + 3) = (9 + 3) = 12.
∴ Breadth will be x = 9.
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Simplify: -42 30(cubed) / 12 10 (cubed)
The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.
If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.
Simplify: -42 30(cubed) / 12 10 (cubed)?
By removing the denominators, convert fractions to integers.
Because the denominators of our two fractions differ, we must calculate the Least Common Denominator and rewrite our fractions using the common denominator as needed. LCD(-42/30, 12/10) = 30
Now that the denominators of our two fractions are similar, we may multiply them both by 30 to get rid of the denominators.
The final result is: -42/30: 12/10 = -42: 36
With the highest common factor, attempt to further reduce the ratio (GCF).
GCF is 6 for -42 and 36.
Divide both terms by the GCF, 6, as follows: -7 36 6 = 6; -42 6 =
By dividing both parts by the GCF = 6, the ratio -42:36 can be reduced to its smallest terms: -42:36 = -7:6.
Therefore:
-42/30 : 12/10 = -7 : 6
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y=x² + 2x - 2
iii) Find the values of x
when y = 2
Answer: 1.236, -3.236 or [tex]-1-\sqrt{5} and -1+\sqrt{5}[/tex]
Step-by-step explanation:
2 = x^2 + 2x -2
x^2 + 2x - 2 -2
x^2 +2x -4
put into quandratic formula
The PTA at a school want to sell chocolate bars to support the school PTA. They asked a random sample of 10 students how many chocolate bars they would be willing to buy at a price of $2 for each bar. Their responses are summarized in the following dot plot:
If there are a total of 250 students at the school and the sample is representative of the entire school's population of students, which of the following is the most reasonable estimate of the total number of chocolate bars the PTA can expect to sell to all the students of the school? A. 250
B. 500
C. 600
D. 750
Answer:
B
Step-by-step explanation:
the most answered was 2. 2x250=500
the city of raleigh has 7600 registered voters. there are two candidates for city council in an upcoming election: brown and feliz. the day before the election, a telephone poll of 250 randomly selected registered voters was conducted. 128 said they'd vote for brown, 101 said they'd vote for feliz, and 21 were undecided.
This sample statistic suggests that we might expect 2833 of the 7,600 registered voters to vote for Brown.
Due to that, There are 7,600 registered voters in Raleigh. Brown and Feliz are the two candidates running for city council in the upcoming election. A telephone survey of 550 randomly chosen registered voters was performed the day before the election. 205 people declared they would support Brown, 317 people would support Feliz, and 28 people were unsure.
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown can be calculated as follows:
p = 205/550 =0.3727
Expected number of voters who vote for Brown:
The expected number of voters who vote for Brown can be calculated as follows:
E voters who vote for Brown =7600 *0.3727=2832.52= 2833 (Approx.)
This sample statistic suggests that we might expect 2833 of the 7,600 registered voters to vote for Brown.
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if a regression model is constructed from the data given here, what is the residual for the prime interest rate of 8%? bond rate in 5% 12% 9% 14% 7% prime interest rate 14% 6% (x) 8% 5% 7% o a 11.12 o b.-5.16 o cobb od.-0.88
The residual for the prime interest rate is 0.88.
What is a regression equation?
An equation created to explain the relationship between independent and dependent variables is known as an estimated regression equation in statistics.
The relationship between the dependent and study variables is first hypothesized using a simple or multiple regression model. The most popular technique for creating estimates of the model variables is the least squares method.
Predicting the worth of the dependent variable while values for the predictor factors are known is one of the main uses of both the estimated regression equation.
From the given regression model,
n = 5
∑X = 40
∑Y = 47
∑XY = 333
∑X² = 370
n∑X.Y - ∑X.∑Y = -215
n∑X² - (∑X)² = 250
∑Y.∑X² - ∑X∑XY = 4070
FOR REGRESSION EQUATION
a= ( ∑Y.∑X² - ∑X∑XY )/ (n∑X² - (∑X)² ) = 16.28
b = (n∑X.Y - ∑X.∑Y) / (n∑X² - (∑X)² ) = -0.86
ŷ = b x + a = -0.86 x + 16.28
predicted value at x = 6 ;
ŷ = (-0.86 * 6) + 16.28 = 11.12
Residual = y - ŷ = 12 – 11.12 = 0.88
The residual for the prime interest rate is 0.88.
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tacoma's population in 2000 was about 200 thousand, and has been growing by about 9% each year. if this continues, what will tacoma's population be in 2010?
4,31,784.999454 will be the population of Tacoma in 2010 .
What is exponents ?The exponent of a number is the number of times it is multiplied by itself.
Positive, negative, zero, and rational/fractional exponents are the four kinds.
The value of the number may be deduced from the exponent, which is the total number of times the base number must be multiplied by the same base.
CalculationIf the population at the beginning of 2000 was 200,000
Then the growth equation is P = Po(1.08)(y) where year year 2000 was year 1 or y = 1
At the end of 2015 or 2010-2000 = 15 years later, or at the end of the 15th year:
Population P(10) = (200,000)(1.08)10 = 4,31,784.999454
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The half-life of a radioactive
substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. Carbon 14 has a half-life
of 5730 years. Suppose given samples of carbon 14 weigh 5/8 of a pound and 7/8 of a pound. What was the total weight of the samples 11,460 years ago?
The total weight of the samples 11,460 years ago is 6 pounds
What is Exponents?
Exponentiation is a mathematical process that involves the base b and the exponent or power n. It is represented as b^n and is pronounced as "b to the n."
The exponential process of radioactive decay is depicted by
[tex]A_{t}[/tex] =[tex]A_{0}[/tex] [tex]e^{-kt}[/tex]
where = Amount of the radioactive element after t years
[tex]A_{0}[/tex] = Initial amount
k = Decay constant
t = time in years
The carbon-14 half life is 5730 years.
[tex]A_{0}[/tex]/2 = [tex]A_{0}[/tex][tex]e^{-5730k}[/tex]
1/2 = [tex]e^{-5730k}[/tex]
At this point, we take ln (Natural log) on both sides.
ln(1/2) = ln [ [tex]e^{-5730k}[/tex]]
-ln(2) = -5730kln(e)
0.69315 = 5730k
k = 0.69315 / 5730
k = 1.21 x [tex]10^{-4}[/tex]
We now need to determine the weight in pounds of the C-14 samples that were taken for the remaining quantities.
5/8 =[tex]A_{0}[/tex] [tex]e(^{-1.21 * 10^{-4} * 11460})[/tex]
5/8 = [tex]A_{0}[/tex] [tex]e(^{-1.3863})[/tex]
[tex]A_{0}[/tex] = (5/8) [tex]e(^{-1.3863})[/tex]
[tex]A_{0}[/tex] = 5/8 x 4
[tex]A_{0}[/tex] = 5/2
[tex]A_{0}[/tex] = 2.5pounds
Similarly for 7/8 pound
7/8 = [tex]A_{0}[/tex] [tex]e(^{-1.21 * 10^{-4} * 11460 })[/tex]
7/8 = [tex]A_{0}[/tex] [tex]e(^{-1.3863 })[/tex]
[tex]A_{0}[/tex] = (7/8) [tex]e(^{-1.21 * 10^{-4} * 11460 })[/tex]
[tex]A_{0}[/tex] = 7/8 x 4
[tex]A_{0}[/tex] = 7/2
[tex]A_{0}[/tex] = 3.5 pounds
Hence, The total weight of the samples 11,460 years ago 2.5 + 3.5 = 6pounds
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a college has over 5{,}0005,0005, comma, 000 students, 10\, percent of which are left-handed. a new lecture hall is being planned that will seat 300300300 students, and college officials want to be sure there are enough left-handed desks. suppose we randomly select groups of 300300300 students from this college. what are the mean and standard deviation of the number of left-handed students in each group of 300300300? you may round your answers to the nearest tenth.
The mean of the given data is 30 students and the standard deviation is 5.2.
What is standard deviation?
The standard error of either a statistic (such as the sample mean) and the standard deviation of a sample or population are fundamentally separate but related concepts.
The standard deviation of the collection of means that would be discovered by taking an unlimited number of multiple samples from the population and calculating a mean for each sample is the sampling mean's standard error.
The sample standard deviation reduced by the sample size is used to estimate the mean's standard error, which turns out to be equal to the population variance times the square root of the random sample.
Given that,
5,000 students, 10 % of which are left-handed.
A new lecture hall is being planned that will seat 300 students.
The mean is 30 students
standard deviation is 5.2 students
The mean of the given data is 30 students and the standard deviation is 5.2.
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F(2,9) after a reflection over the y-axis.
Answer:
(-2, 9)
Step-by-step explanation:
hope it helped <3333 :D
How do you solve (x+3)^2=121? Sorry it's been a while...
Answer: x = 8
Step-by-step explanation:
(x + 3)^2 = 121
Take the square root of both sides
x + 3 = 11
x = 8
Plug it back in to double check
(8 + 3)^2 = 121
(11)^2 = 121
121 = 121
What is the 10th term of the sequence 5,2, 4/5,….
Good evening,
Answer:
-512/390625
Step-by-step explanation:
an=a1 •r^n-1
a10=5 • -0.4^10-1
a10=5 • -0.4^9
a10=5 • -512/1953125
a10= -512/390625
Simplify 3/8 (16 R +32)
a 8R +12
B 48R +96
C 120R +256
D 42R +85
Answer:
6R+12
Step-by-step explanation:
Your options are wrong maybe...
3/8(16R+32)
= 6R+12
(a) The perimeter of a rectangular garden is 292 m.
If the length of the garden is 89 m, what is its width?
Width of the garden: ?
(b) The area of a rectangular window is 7968 cm².
If the width of the window is 83 cm, what is its length?
Length of the window: ?
Answer:
(a) Let width of garden be w m.
Perimeter = length + width + length + width
Substitute the values into the equation.
89 + w + 89 + w = 292
Simplify and solve for w.
2w + 178 = 292
2w = 114
w = 57
Hence, width of garden is 57 m.
(b) Let length of window be L cm.
Area = length × width
Substitute the values into the equation.
L × 83 = 7968
Simplify and solve for L.
83L = 7968
L = 96
Hence, length of window is 96 cm.
in a multiple regression analysis involving two independent variables, if b1 is computed to be 2.0, it means that
In a multiple regression problem involving two independent variables X1 and X2, if b1 is computed to be +2.0, it means that. the relationship between X1 and Y is significant .
What is multiple regression analysis?Multiple regression is a statistical method that may be used to assess a single dependent variable and several independent variables. Multiple regression analysis use known independent variables to anticipate the value of a single dependent variable. Each predictor value is assigned a weight, which indicates how much each predictor contributed to the overall forecast.
CalculationIn a multiple regression problem involving two independent variables X1 and X2, if b1 is computed to be +2.0, it means that. the relationship between X1 and Y is significant .
The estimated value of Y increases by an average 2 units for each increase of 1 unit of X1, holding X2 constant.
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(y-1.1)(-3y)
= (y) ( ) ( ) (-3y)
= -3y __ __ 3.3
i feel like god oo yeah i feel like god oo yeah take my glasses of i can seethm
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Step-by-step explanation:eeeezzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
If the quadratic formula is used to find
the roots of the equation 2x² - 5x - 12
= 0, then what are the correct roots?
The two roots obtained for the quadratic equation by quadratic formula are 1.5 and 4.
What is defined as the quadratic formula?A quadratic equation is just a polynomial with a second degree first term. There are several methods for determining the roots, or solutions, of such a quadratic equation. Every quadratic equation has two solutions, that might or might not be real numbers. The quadratic formula is a simple method for resolving a quadratic equation. whether the answer is a whole number, an irrational number, or perhaps an imaginary numberIf the quadratic equation is ax² + bx + c = 0.
Then, the roots are given by x = [-b ± √(b² - 4ac)]/2a.
The quadratic equation is given as; 2x² - 5x - 12 = 0.
On comparing with the standard form;
a = 2b = -5c = -12Put the values in the formula,
x = [-b ± √(b² - 4ac)]/2a.
x = [-(-5) ± √((-5)² - 4×2×(-12))] / 2×2
On simplification,
x = [5 ± 11]/4
There will be two roots of equation,
a; x = [5 + 11]/4
x = 16/4 = 4
b ; x = [5 - 11]/4
x = 6/4 = 1.5
Thus, the two roots obtained for the quadratic equation by quadratic formula are 1.5 and 4.
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There may be more then one answer
Will give brainlest
Help please! :)
Directions: Answer each question below, showing all pertinent work.
Solve all using Estimate.
A. –42.3 ÷ 3.4
B. 16.1 – (–14.7)
C. –15.52 + 54.25
D. ‐67.8 ‐ 5.72
1.Brock had $3084 in his checking account. He wrote checks for $350 for rent, $275 for auto repair, and
$169 for a loan payment. Find the amount remaining in his account.
2.Linda’s paycheck was for $2312. She spent $157 on rent, $322 on food, $478 on child care, $234 on
transportation, and $290 on other things. She put the rest of her paycheck in savings. How much did
she put in savings?
A1) Using estimate, the solutions to the following are:
A) is -14.
B) is 31.
C) is 38.
D) is -74.
1. The remaining amount in Brock's account after writing the checks is $2,290.
2. Linda put $831 in her savings account after meeting her expenses.
What is an estimate?An estimate is a rough calculation.
To do an estimate, the figures may be appropriated or rounded up.
Estimates:A. –42.3 ÷ 3.4
= -14 (–42 ÷ 3)
B. 16.1 – (–14.7)
= 31 (16 – (–15)
C. –15.52 + 54.25
= 38 (–16 + 54)
D. ‐67.8 ‐ 5.72
= -74 (‐68 ‐ 6)
Brock:The amount in Brock's checking account = $3,084
Checks:
Rent $350
Auto repair $275
Loan payment of $169
Total amount for checks = $794
Remaining amount = $2,290 ($3,084 - $794)
Linda:The total amount of the paycheck = $2,312
Expenses:
Rent $157
Food $322
Child care $478
Transportation $234
Miscellaneous expenses $290
Total expenses = $1,481
Savings account = $831 ($2,312 - $1,481)
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Make an equation for the first question
Then use the equation to find the cab fare if zarela has a 1.8 mile commute to work
The two equations are : 6x + m = F
and 6x + 1.8 m = F
How to solve a linear equations ?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b)
Let the total time be x
Given distance Zarela travels is m
Thus the total cab fare = F
Therefore the equation becomes;
6x + m = F
In the second part of the question it is given that Zarela travels for 1.8 mile
thus the equation becomes
6x + 1.8 m = F
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