Gary, Mary, and Rory have 96 candies altogether.
Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".
After Gary gives Mary half of all his candies, he would have x/2 candies.
Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.
And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.
Now, we know that Gary would have 12 more candies than he had originally, which means:
x/2 + x/8 = x/2 + x/4 - 12
We can combine like terms and simplify the equation:
x/2 + x/8 = x/4 + x/4 - 12
x/8 = 12
x = 8 * 12
x = 96
Thus, Gary, Mary, and Rory have 96 candies altogether.
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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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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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What will be the mirror image of − 3 − 4 in y-axis?
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 solution of 3 root?
Answer: 1.442
Step-by-step explanation:
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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7. Mai and Tyler are selling items to earn money for their elementary school. The school
earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai
sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10
wreaths and 7 potted plants and the school earns $62.50.
This situation is represented by this system of equations:
[ 14w + 3p = 70.50
10w+7p = 62.50
Explain why it makes sense in this situation that the solution of this system is also a
solution to 4w + (-4p) = 8.00.
On solving the provided question we can say that - her in the equation 14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18
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.
[tex]14w + 3p = 70.50 \\[/tex]
10w+7p = 62.50 ,
[tex]w = 12\\[/tex]
p = 18
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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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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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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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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
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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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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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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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)?
which postulate proves these two triangles are congruent
The given triangles are congruent by SAS criteria.
What are congruent triangles?Congruent triangles have both the same shape and the same size.
Given are two right angled triangles as shown in the image.
In the right angled triangles -
Two corresponding sides are equal.
They both have one right angle common.
We can conclude them as congruent by SAS Rule.
Therefore, the given triangles are congruent by SAS criteria.
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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°
Do you remember all 4 ways to solve a quadratic equation?
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.
what is quadratic equation ?A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.
given
Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.
Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)
Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.
The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.
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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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Marc's brownie pan, shown below, has a pair of parallel sides. Each day, Marc's family is going to eat 100 square centimeters of brownie from the pan. For how many days does Marc's family have brovnics before they run out? top:29 bottom: 41 side : 20
Determine how many square centimeters make up a square meter in order to determine how long Marc will have brownies before they run out.
How to calculate a square meter?We must first determine the number of square centimeters in a square meter in order to determine how many days Marc has left of brownies before they run out. A square meter has 3.6 square meters in it.
Because of this, Marc has access to brownies for 3.6 days until they are finished.
Knowing the dimensions of a square or rectangle will allow you to compute its square meters. Also known as the shape's area, this term is used. Length times width equals m2, which is the formula used to calculate square meters. As an illustration, if your square is 3 meters long and 2 meters wide, 3 x 2 equals 6 meters2.
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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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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:
26 °
100°
X=
help anyone ?
Answer:
Step-by-step explanation:
26° + 100°
= 126°
360° - 126°
234°
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]
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
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
Are 3x-2 and 3x2 reciprocals? Explain.
Answer: No, 3x-2 and 3x^2 are not reciprocals.
Step-by-step explanation: The reciprocal of a number is defined as the multiplicative inverse of that number, which means that when a number is multiplied by its reciprocal, the result is 1. For example, the reciprocal of 2 is 1/2, because 2 * (1/2) = 1.
In contrast, 3x-2 and 3x^2 are not numbers, they are expressions that contain variables. It is not possible to determine their reciprocals without knowing the values of the variables.
For example, if x=1, then the reciprocal of 3x-2 would be (1/3)/(1-2) = -1/3, and the reciprocal of 3x^2 would be (1/3)/(1^2) = 1/3. However, if x=2, then the reciprocal of 3x-2 would be (1/3)/(2-2) = undefined, and the reciprocal of 3x^2 would be (1/3)/(2^2) = 1/12.
So it is not accurate to say that 3x-2 and 3x^2 are reciprocals.
No
The only thing stopping these from being reciprocals is the -2. Say x becomes 3
First we get 3(9)-2.
Next, we'd get 3(3)(2)
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
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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