In 100 students, Science was rated favorably by 25 students, while math received ratings from 41 students. 19 of the students polled indicated that they approved of both. 16 students are the complement of math.
What is complement of a number?The phrase "complement" is typically used to describe a subset of a set that does not include another subset. The entire original set is obtained by adding the complement and its taking. The complement of a set is typically represented by the notations. The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.
The Total number of students were 100
Students who like maths were 41
Students who like science were 25
Students who like both maths and science were 19
Students who does not like maths are 41-25 = 16.
So the students who are the complement of math are 16.
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show a²-4= (a+ 2)(a-2) in diagram
The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
What is Factorization?Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.
In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.
Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.
Given:
The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).
This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
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Tierra is making steps for a doll house. She has cut a piece of wood that measures 1. 5 centimeters wide and 30 centimeters long. Each step will measure 15 millimeters by 4 millimeters. She will make 21 steps for her doll house. Which are the dimensions of the wood that remains after Tierra finishes making the 21 steps?
The dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm
In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape.
A square has sides of equal dimensions.
A rectangle has length and width as its dimensions that define the area of a rectangle.
Also, dimension is used widely to term the figure as one-dimensional, two-dimensional or three-dimensional.
Wood = 1.5 cm by 30 cm
Each cut = .15 mm by 4 mm
Steps = 21
The remaining dimension is calculated as:
Remaining = 1.5 cm - 21 * .15 mm by 30 cm - 21 * 4 mm
Express mm as cm
Remaining = 1.5 cm - 21 * .015 cm by 30 cm - 21 * 0.4 cm
Evaluate the difference
Remaining = 1.185 cm by 21.6 cm
Hence, the dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm
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how do i answer part b
Answer: The slope is the cost per hour (in this case $20 per hour).
=========================================================
Further Explanation:
Recall that,
[tex]\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}[/tex]
The rise tells us how much to go up or down, depending if the rise is positive or negative. The run tells us how much to go to the right. Always move to the right.
In this problem, the change in y is the change in price. The change in x is the change in hours. Dividing the two items gives cost per hour, aka unit cost.
-----------------------
Example:
Let's pick two points from this line and use the slope formula. I'll pick (1,60) and (3,100) as they are the only two points with coordinate labels.
So,
[tex](x_1,y_1) = (1,60) \text{ and } (x_2,y_2) = (3,100)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{100 - 60}{3 - 1}\\\\m = \frac{40}{2}\\\\m = 20\\\\[/tex]
The slope is 20, or 20/1
It says that each time the number of hours x goes up by 1, the cost variable y goes up by 20.
Put simply: The hourly fee is $20 per hour.
This matches what it says in the instructions when your teacher wrote "A roofer charges $60 for the first hour and $20 per hour for each additional hour".
Miss Jennifer is buying pencils in packs of 12, notebooks in packs of 16, and red pens in boxes of 20. She needs to have the same number of pencils, notebooks, and red pens. How many packs of each type should she buy?
someone pls help
She needs to purchase 240 packets of each kind in order to have an equal amount of pencils, notebooks, and red pens.
what is LCM ?Least Common Multiple is referred to as LCM. The smallest number that is a multiple of both numbers is the least common multiple of the two. The first few multiples of each integer should be listed.
Look for duplicates that appear on both lists. Write out additional multiples for each number if the lists don't contain any common multiples. The least integer shared by both lists should be found. The LCM is this figure.
given
This entails determining the 16, 12, and 20 Least Common Multiples (LCM).
2⁴ = 16 = 2 * 2 * 2 * 2
2²*3 = 12 = 2 * 2 * 3
2²*3 = 12 = 2 * 2 * 3
2²*5 = 2 * 2 * 5
Keep in mind that LCM is the prime factorization of the involved integers multiplied by the highest power of each prime factor;
22 * 3 * 5 = 240.
She needs to purchase 240 packets of each kind in order to have an equal amount of pencils, notebooks, and red pens.
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What is the reflection point of (- 3/4 across the line y 2?
According to the following graph, the reflection point of (-3,4) across the line y = 2 is (-3,0).
The term reflection point in math is defined as
Here we need to find the reflection point of (-3, 4) across the line y = 2.
Here first we have t plot the point on the graph, and then we have to plot the line equation y = 2 on the graph,
Here in order to find the reflection of a point along the x-axis, then we have to keep the abscissa constant and see the reflection of ordinate along the x-axis.
Based on these rule, the resulting graph is obtained as follows.
Through the graph we have identified that the resulting reflection point is (-3,0).
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Which expression is not equivalent to logp 36? 1. 6 log 2 2. log 9+ Iog, 4 O 3 2 logb 6 4. log 72 logp 2
log 30+ log 6 is not equivalent to log 36
What is equivalent expressions?Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).
The original phrase is as follows
Log 36
Following that, we write the alternatives (a) log 2+ log 18
Apply the logarithmic rule log 2+ log 18 log (218)
Log 2 plus log 18 log (36)
Remove the bracket
Log 2 plus log 18 log36
(a) Log 2+ Log 18 is the same as log 36.
(b) Log 30 plus log 6
Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)
Log 30 plus log 6 Equals log (180)
Remove the bracket
Log 30-plus log 6-log180
Hence,
(c) Log 30+log 6 does not equal log 36.
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What will be the mirror image of − 3 − 4 in y-axis?
Hilda filled her aquarium with
water. On Monday, she put 8 cups
into the aquarium. On Tuesday she
put 2 pints. On Wednesday, she put
quarts. How many cups of water dic
she put into her aquarium in all?
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable. A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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Evaluate the iterated integral. π/2 0 x 0 x sin(y) dy dx
The answer to the iterated integral after the evaluation is 2.
The iterated integral evaluates to the area of the region bounded by the curves x = 0, x = y, and y = π/2, which can be calculated by setting up a double integral. The outer integral is with respect to x, from 0 to π/2, and the inner integral is with respect to y, from 0 to x.
The integrand is xsin(y), meaning that the area of the region is the integral of xsin(y) with respect to y from 0 to x, and then with respect to x from 0 to π/2. The solution is found by evaluating the inner integral first, which yields -xcos(x), and then evaluating the outer integral. The result is 2, which is the area of the given region.
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this diagram shows 3cm x 5 cm x 4 cm cubiod
find ac give your answer in 2 decimal place
The length AC will be 5.83 and the angle ACD will be 34.45°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
The length AC will be calculated as,
AC² = 5² + 3²
AC = √ ( 25 + 9 )
AC = √34
AC = 5.83
The angle ACD will be,
tanθ = P / B
θ = tan⁻¹ = ( 4 / 5.83)
θ = 34.45°
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what is the product of 69 and 5.6 x 10^5 expressed in scientific notation
[tex](69)(5.6\times 10^{5})\implies (69)(560000)\implies 3\underset{\leftarrow 7\to }{\underline{8640000}}\implies 3.864\times 10^{7}[/tex]
A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is
A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is (0.2301, 0.2759).
How to find a confidence interval for a population proportion?A part of a population with a particular attribute, expressed as a fraction, decimal or percentage of the whole population. For a finite population, the population proportion is the number of members in the population with a particular attribute divided by the number of members in the population.A proportion is a part, share or number considered in comparative relation to a whole. It can be equal to 0, 1 or any value between 0 and 1. It can be expressed as a number or percentage. One example in official statistics would be the proportion of the Canadian population who lives in a given province.p′ = x / n where x represents the number of successes and n represents the sample size. The variable p′ is the sample proportion and serves as the point estimate for the true population proportion.A population proportion is a fraction of the population that has a certain characteristic. For example, let's say you had 1,000 people in the population and 237 of those people have blue eyes. The fraction of people who have blue eyes is 237 out of 1,000, or 237/1000.(0.2301, 0.2759).
This interval is calculated using the following formula:
(sample proportion - margin of error, sample proportion + margin of error)
Where the sample proportion is the number of favorable voters (100) divided by the sample size (432), and the margin of error is calculated using the standard error and a critical value from a normal distribution table.
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An electronics store owner is trying to how much they should try to sell a computer that cost the store $200. They want to increase this price by 25% for the store’s profit and then increase that new price by 15% to account for the sales person’s profit. How much should they sell the computer for?
Answer:
They should sell the computer for $287.50
Step-by-step explanation:
Let's solve the 25% increase first
100% = $200
100% + 25% = 125% = 1.25
200 x 1.25 = $250
Then we find the 15% increase
100% = $250
100% + 15% = 115% = 1.15
250 x 1.15 = $287.50
So, they should sell the computer for $287.50
NEED HELP DUE TOMORROW PLS!!!!!!
The cost of filling the cone to its full capacity would be = 189.4 cents
What is a cone?A cone is a three-dimensional figure in geometry that tapers from a flat base (usually a circular base) to a point called a vertex or longitude (which forms an axis through the center of the base).
The formula for the volume of a cone = πr²h/3
Height (h) = 5 inches
Radius (r) = 3 inches
π = 3.14
volume = 3.14 × 3² × 5/3
= 3.15 × 9 × 1.67
= 47.35 in³
But 1 in³ = 4 cents
47.35 in³ = X
Make X the subject of formula;
X = 47.35 × 4 = 189.4 cents.
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9 people audition for a choir. The choir director must choose one soprano, one alto,
and one tenor.
In how many ways can the director fill these positions?
The numbers of ways that the director fill these positions is 504 ways.
What is the position about?There are a few different ways to approach this problem, but one possible method is to use the combination formula.
To fill the position of soprano, the director has 9 choices. After selecting one soprano, the director is left with 8 singers to choose from for the alto position. Then, the director has 7 singers to choose from for the tenor position.
So, the total number of ways the director can fill these positions is:
9 × 8 × 7
= 504 ways.
Alternatively, One can also use the permutation formula to solve the question. The formula of permutation is (n!/(r!(n-r)!)), where n is the total number of items to choose from, and r is the number of items to be chosen.
For this case n is 9, and r is 3, so the permutation would be:
(9!/(3!(9-3)!)
= (987)/(321)
= 504
Therefore, In both cases, the answer is 504 ways.
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Determine the Domain and Range of each graph, then decide if the graph is exponential growth or decay.
The required,
1. figure 1, domain and range are (0, ∞) and {25000, 0}, the graph shows the exponential decay.
2. figure 2, domain and range are (-∞, ∞) and {0, ∞}, the graph shows the exponential growth.
The function which is in format f(x) =aˣ where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
As mentioned in the question, the graph of two exponential functions are given, we have to determine the domain and range of both function and justify which graph shows the exponential growth and decay.
1.
A general exponential equation is given as,
y = aˣ
Graph 1, the graph shows the exponential decay because the value of the function is getting decreasing for the domain 0 to ∞. For this domain, the value of the function starts from point A which is at 25000 and ends at point B where y = 0, so the range is {25000, 0}.
Similarly,
Graph 2 shows exponential growth,
Domain and range are (-∞, ∞) and (0, ∞).
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HELP!
4(2x-3)=6x+2
I thought when I simplify it 22x=14 but its wrong
Answer:
the answer is 1
Step-by-step explanation:
4(2x-3)=6x+2
8x-12=6x+2
+6x +6x
14x-12 =2
+12 +12
14x=14
x=1 and don't worry we all make mistakes
-50 POINTS-
Don’t need to explain
A.)
B.)
C.)
Answer:
C
Step-by-step explanation:
30PTS 30PTS don’t explain just answer
Answer:
y = 95°
Step-by-step explanation:
x + 120° = 180°
x = 180° - 120°
x = 60°
25° + y + x = 180°
25° + y + 60° = 180°
y + 85° = 180°
y = 180° - 85°
y = 95°
How to do plotting points?
Place a dot at the origin, sometimes referred to as the center of the Cartesian coordinate axis, to begin. We may then plot a point on the graph after placing the necessary points there.
An x-y (or bivariate) plot is any graph or plot with two axes.
The "x-axis" is often the horizontal axis, whereas the "y-axis" is typically the vertical axis.
However, if you have a data set with two sets of related data, you may utilize any variable for either one.
There are a few procedures you may take when plotting data on a graph to make sure you don't neglect anything:
Make sure you are working with two variables (two columns of data).
Make a decision on which variable will be represented on the x-axis and which on the y-axis.
Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled).
Plot the first two pairs of numbers first (the top row of numbers).
Plot pairs of points repeatedly until all the points have been plotted.
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Some help please!!!!
Step-by-step explanation:
what do you not understand ? please let me know where you need more instructions.
the basic rule : every term of one side has to be multiplied with every term of the other side, and the results are added (by using the correct signs of the products).
remember :
+ × + = +
- × - = +
+ × - = -
- × + = -
(3x - 3)(5x - 4) = 3x × 5x + 3x × -4 + -3 × 5x + -3 × -4 =
= 15x² - 12x - 15x + 12 = 15x² - 27x + 12
What value of x satisfies the equation − 3 4x − 5 )= 2 1 − 5x?
For the given expression, x has a value of 6.5.
What are expressions?A sentence qualifies as a mathematical expression if it comprises one or more mathematical operations, at least two numbers, or variables.
A number is 6 times larger than the other number, x, by a factor of 2.
The equation x/2 + 6 in mathematics represents this claim.
Here, we have the equation:
-3(4x - 5) = 2(1 - 5x)
Find the value of x by solving the expression:
-3(4x - 5) = 2(1 - 5x)
-12x + 15 = 2 - 10x
-2x = -13
x = -13/-2
x = 13/2
x = 6.5
Therefore, for the given expression, x has a value of 6.5.
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Correct question:
What value of x satisfies the equation -3(4x - 5) = 2(1 - 5x)?
The solution process is shown for an equation. Justify each step in the process with the appropriate property. Select the correct answer from each drop-down menu. 2 ( 3 y + 4 ) − 3 ( y − 2 ) = 2 y original equation 6 y + 8 − 3 y + 6 = 2 y 3 y + 14 = 2 y combining like terms 14 = - y - 14 = y y = - 14
All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equation is given below.
2(3y + 4) − 3 (y − 2) = 2y
Simplify the equation, then we have
2(3y + 4) − 3 (y − 2) = 2y
6y + 8 − 3y + 6 = 2y
3y + 14 = 2y
14 = 2y - 3y
14 = - y
y = - 14
All the steps of the solution are written above. Then all the options are correct. And the solution is - 14.
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PLS HELP ME I ONLY HAVE 2 MINS TO ANSWER!!!!!!!!! ITS 100 PTS!!!!!
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Week 1 Week 2 Week 3
Salesman A 11 14 16
Salesman B 14 15 13
Salesman C 16 12 11
In which week(s), did Salesman C have a larger paycheck than both of the other salesmen? Select all that apply.
Week 3
None of the weeks.
Week 2
Week 1
In Week 1,
Salesman C got larger paycheck than Salesman A and Salesman B.
What is equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions
The sign that connects these two expressions is “=”.
In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.
Given,
Commission of salesman A per sale = $65
Commission of salesman B per sale = $40
Commission of salesman C per sale = $0
Salary of salesman A per week = $0
Salary of salesman B per week = $300
Salary of salesman C per week = $900
No. of sales × commission + salary = total earning
In week 1.
Earning of A
11 × $65 + $0 = $715
Earning of B
14 × $40 + $300 = $860
Earning of C
16 ×$0 + $900 = $900
In week 2.
Earning of A
14 × $65 + $0 = $910
Earning of B
15 × $40 + $300 = $900
Earning of C
12 ×$0 + $900 = $900
In week 3.
Earning of A
16 × $65 + $0 = $1040
Earning of B
13 × $40 + $300 = $820
Earning of C
111 ×$0 + $900 = $900
By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.
In week 2 and week 3 his paycheck is smaller than both of the other salesman.
Hence, Salesman C received larger paycheck than both of the other salesmen in Week 1.
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Subtract (7x+5)-(3x+2)?
Answer:
Step-by-step explanation:
original equation equivalent to 7x+5-3x-2 = 7x-3x+5-2=4x+3
the answer is 4x+3
Answer:
The answer is 4x+3
Which exponential function has an initial value of 2?
Of(x) = 2(3)
Of(x) = 3(2)
X
-2
-1
f(x)
18
1
4
On solving the provided question, we can say that - here in the equation, [tex]x^2- x = 4[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
so, x = 2
therefore
[tex]x^2- x \\6-2\\4[/tex]
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If an investment company pays 6% compounded continuesly, how much should you deposit now to have $10,000 5 years from now?
The amount of money should you deposit now to have $10,000 5 years from now is $7407.
What is compound interest?Theoretically, continuously compounded interest means that interest is continuously earned on an account balance as well as reinvested into the balance to increase future interest earnings.
Given that If an investment company pays 6% compounded continuously and $10,000 for 5 years.
The amount of money invested will be calculated by the formula below,
[tex]P = P_o(e)^{rt}\\10000 = P_o ( e)^{0.06\times5}\\[/tex]
P₀ = 10000 / 1.35
P₀ = 7407
The amount of money invested would be 7407.
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What is the solution of 3 root?
Answer: 1.442
Step-by-step explanation:
The pairs of polygons below are similar. Give the scale factor of figure A to figure B.
1/8
2
1/4
8
1/2
4
From figure A to figure B, the scale factors are 1/8 and 1/2. To scale shapes in various dimensions, utilize the scale factor.
what is polygon ?A polygon is a closed object in a two-dimensional plane comprised of line segments rather than curves. The word "polygon" is a combination of the words "poly" (which meaning many) and "gon" (means sides). A closed figure must include a minimum of three line segments that connect end to end. A polygon is any three or more-sided closed two-dimensional shape. In addition to more complex designs like a dodecagon with twelve sides, polygons include triangles and squares. Polygons include shapes like quadrilaterals, triangles, hexagons, and pentagons. The number of sides the form has is indicated by the name.
given
the scale factor of figure A to figure B
= smaller dimension / larger dimension
= 2/16
= 1/8
and 4/8
= 1/2
From figure A to figure B, the scale factors are 1/8 and 1/2. To scale shapes in various dimensions, utilize the scale factor.
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Eleven is 20% of what number?
55
11 = 20% × y
11 = 20/100 × y
multiply both sides by 100 and divide both sides by 20
y = 11 x 100/20
y = 11 × 100 ÷ 20
y = 55