Final answer:
To simplify 50% of one-twentieth of the product of 12 and 5z plus 5, you first calculate the product (60z), take one-twentieth (3z), find 50% of that (1.5z), and then add 5 to get the simplified expression 1.5z + 5.
Explanation:
The question asks to simplify the expression 50% of one-twentieth of the product of 12 and 5z plus 5. Here are the steps to simplify this expression:
Firstly, calculate the product of 12 and 5z, which is 60z.
Then, find one-twentieth of this product, which is 60z / 20 = 3z.
50% of 3z is 1.5z.
Finally, add 5 to 1.5z, which gives you 1.5z + 5 as the simplified expression.
So, the simplified expression is 1.5z + 5.
50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]
To calculate 50% of one-twentieth of the product of [tex]\(12\) and \(5z + 5\)[/tex], we'll follow these steps:
Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\)[/tex].
[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]
Step 2: Calculate one-twentieth of the product.
[tex]\[ \text{One-twentieth of the product} = \frac{\text{Product}}{20} \][/tex]
Step 3: Calculate 50% (or half) of one-twentieth of the product.
[tex]{50% of one-twentieth of the product}[/tex] = [tex]\frac{1}{2} \times \frac{\text{Product}}{20} \][/tex]
Now, let's perform the calculations step by step:
Step 1: Calculate the product of [tex]\(12\) and \(5z + 5\):[/tex]
[tex]\[ \text{Product} = 12 \times (5z + 5) \][/tex]
[tex]\[ = 12 \times 5z + 12 \times 5 \][/tex]
[tex]\[ = 60z + 60 \][/tex]
Step 2: Calculate one-twentieth of the product:
[tex]\[ \text{One-twentieth of the product} = \frac{60z + 60}{20} \][/tex]
[tex]\[ = \frac{60z}{20} + \frac{60}{20} \][/tex]
[tex]\[ = 3z + 3 \][/tex]
Step 3: Calculate 50% of one-twentieth of the product:
{50% of one-twentieth of the product} =[tex]\frac{1}{2} \times \left(3z + 3\right) \][/tex]
[tex]\[ = \frac{1}{2} \times 3z + \frac{1}{2} \times 3 \][/tex]
[tex]\[ = \frac{3z}{2} + \frac{3}{2} \][/tex]
So, 50% of one-twentieth of the product of (12) and[tex]\(5z + 5\) is \( \frac{3z}{2} + \frac{3}{2} \).[/tex]
True or false the angle bisector of a triangle could also be the perpendicular bisector
Answer:
true
Step-by-step explanation:
The angle bisector and perpendicular bisector of a triangle are distinct concepts.
False: The angle bisector and perpendicular bisector of a triangle are distinct concepts.
The angle bisector of a triangle divides the opposite angle into two equal angles, while the perpendicular bisector of a segment is a line perpendicular to a segment at its midpoint.
It is possible for the angle bisector of a triangle and the perpendicular bisector of different segments within the triangle to coincide, but in general, they are not the same.
Chris needs $858 to buy a computer. She has already saved $575. She gets $15 an hour for babysitting and will babysit 12 hours in the next month. She can save &8 a week form her allowance. How many weeks of allowance will it take Chris to save enough to buy the computer?
Answer:
It will take Chris 13 weeks of allowance to save enough to buy the computer.
Step-by-step explanation:
Chris needs $858 to buy a computer.
She has already saved $575.
She gets $15 an hour for babysitting and will babysit 12 hours in the next month, then she will get for babysitting:
($15/hour)(12 hours)=$180
Then, Chris will need:
A=$858-$575-$180→A=$103
She can save &8 a week form her allowance, then she will need:
Number of weeks: n = $103 / ($8/week) → n=12.875 weeks
Rounding:
n=13 weeks
Chris will need 13 weeks of saving her allowance to have enough money to buy the computer.
Chris needs to save a total of $858 for a computer and has already saved $575.
To determine how many weeks she will need to save her allowance to purchase the computer, we must first calculate the additional amount she will earn from babysitting.
Chris earns $15 an hour for babysitting and will babysit for 12 hours in the next month, earning her an additional 15 x 12 = $180.
Adding this to her current savings of $575 gives us a total of $575 + $180 = $755.
The remaining amount needed to buy the computer is $858 - $755 = $103.
Since Chris saves $8 per week from her allowance, we divide the remaining amount by her weekly savings to find the number of weeks required: $103 / $8 = 12.875 weeks.
Since partial weeks of savings are not possible, we round up to the nearest whole number, which means Chris will need 13 weeks to save enough from her allowance to buy the computer.
The company also discovered that it costs $25 to produce 2 camera cases, $59 to produce 4 camera cases and $305 to produce 10 camera cases . Find the total cost of producing 5 camera cases
Please help!!!
Answer:
Cost of 5 camera cases is $85.
Step-by-step explanation:
First we need to determine what type of function we're dealing with, is it linear, quadratic or exponential? We can determine this by calculating the first difference.
We can translate the number of cameras to correspond to the x axis and cost to the y axis. By doing this we can come up with the ordered pairs of (2,25), (4,59),(10,305). Let's get the first two ordered pairs and calculate the first difference:
[tex]\frac{59-25}{4-2}=17[/tex]
And now the second and third value:
[tex]\frac{305-59}{10-4}=41[/tex]
Notice how these values do not match, this means that this function is not increasing at a constant rate meaning that this function is not linear. Now let's calculate the second difference:
[tex]\frac{41-17}{10-2}=3[/tex]
This means our function is quadratic with a=3. Remember that generally speaking a quadratic function is such that:
[tex]y=ax^2+bx+c[/tex]
Where a,b,c are coefficients and in this case a=3. Now, let's solve for b and c values by using the coordinates given. Let's use the coordinates (2,25) where x=2 and y=25 and so:
[tex]f(x)=ax^2+bx+c\\\\25=3(2)^2+b(2)+c\\25=3(4)+2b+c\\25=12+2b+c\\13=2b+c\\\\b=\frac{13-c}{2}[/tex]
Now let's solve for "c" by using different coordinates (4,59) where x=4 and y=59 and also use the "b" value that we calculated above and so:
[tex]f(x)=ax^2+bx+c\\\\59=3(4)^2+(\frac{13-c}{2})(4)+c\\59=48+\frac{52-4c}{2}+c\\11=\frac{52-4c+2c}{2}\\11=26-2c+c\\-15=-c\\\\c=15[/tex]
Now that we know the value of "c" we can use the equation for b to solve for b and so:
[tex]b=\frac{13-c}{2}=\frac{13-15}{2}\\\\b=-1[/tex]
So this means in the quadratic equation a=3, b=-1 and c=15 therefore by using the general equation of a quadratic function we obtain or final equation:
[tex]f(x)=ax^2+bx+c\\\\f(x)=3x^2-x+15[/tex]
Since we want to find the total cost of producing 5 camera cases x=5 and so:
[tex]f(x)=3x^2-x+15\\\\f(5)=3(5)^2-(5)+15\\f(5)=75-5+15\\\\f(5)=85[/tex]
And so the cost of 5 camera cases is $85.
2. Sally buys a hand bag. There was a discount of 30%. If Sally paid $20, what was the original price?
Answer:
the original price is $28.57
Step-by-step explanation:
If the discount is 30% then the amount paid is 70% of the original price. Sally paid $20, it is the discounted price, equivalent to 70%.
We need to divide $20 by 70% to get the original price or the 100%.
$20 / 70% = $28.57 original price.
Since the handbag was has discount of 30%, we multiply the original price with the 30% to get the discount value.
$28.57 * 30% = $8.57 discount
To check: deduct the discount from the original price to get the discounted price.
$28.57 - $8.57 = $20
Write an equation for the line that is parallel to the given line and passes through the given point Y= 3x + 2; (1, 3)
m = 3 is the slope of the given line; also its the slope of anything parallel to the given line
(x1,y1) = (1,3) is the given point the parallel line goes through
y - y1 = m(x-x1) .... point slope form
y - 3 = 3(x - 1) .... plug in the given values; solve for y
y - 3 = 3x - 3
y - 3+3 = 3x - 3 + 3
y = 3x + 0
y = 3x
Final Answer: y = 3x
side note: if you plugged in x = 1 it leads to y = 3 which confirms that (x,y) = (1,3) is on this parallel line.
which is the product of 4x^5-6x^4+4x^3-6x^2
Answer:
2 x^2 (2 x - 3) (x^2 + 1)
Step-by-step explanation:
Factor the following:
4 x^5 - 6 x^4 + 4 x^3 - 6 x^2
Factor 2 x^2 out of 4 x^5 - 6 x^4 + 4 x^3 - 6 x^2:
2 x^2 (2 x^3 - 3 x^2 + 2 x - 3)
Factor terms by grouping. 2 x^3 - 3 x^2 + 2 x - 3 = (2 x^3 - 3 x^2) + (2 x - 3) = x^2 (2 x - 3) + (2 x - 3):
2 x^2 x^2 (2 x - 3) + (2 x - 3)
Factor 2 x - 3 from x^2 (2 x - 3) + (2 x - 3):
Answer: 2 x^2 (2 x - 3) (x^2 + 1)
Answer:
[tex]2x^{2} (2x-3)(x^{2} +1)[/tex]
Step-by-step explanation:
pls answer its 10 points.
Answer: Choice A)
y + 3 = (2/3)(x - 5)
====================================================
Explanation:
Point slope form is
y - y1 = m(x - x1)
m = 2/3 is the given slope
(x1,y1) = (5,-3) is the point the line goes through
So we have
y - y1 = m(x - x1)
y - (-3) = (2/3)(x - 5)
y + 3 = (2/3)(x - 5)
862.4×0.03? A.25.872 B.258.720 C.2587.200 D.25,872.000
Answer:
A) 25.872
Step-by-step explanation:
A tip when multiplying numbers that are decimals, make the numbers whole numbers without decimals:
862.4 * 10 = 8624
0.03 * 100 = 3
8624 * 3 = 25,872
Then divide by the amount you multiplied the numbers by:
25,872 ÷(100 * 10) = 25.872
So your answer is A) 25.872
Answer:
25.872
Step-by-step explanation:
you just line up the desimals and do your regular multipication.
HELPP WILL MARK BRAINLYEST
Which inequality shows the following statement? The theater can hold no more than 250 people.
A. c > 250
B. c <_ 250
C. c < 250
D. c >_ 250
Answer:
B. c <_ 250
Step-by-step explanation:
NO MORE THAN 250 = AT MOST 250 = less or greater than.
PLEASE HELP ME!
-----------------------------------
For the 1st question, the answer is A) Distributive Property:
The reason why Step 1 is A) Distributive Property is because you're distributing 2 to the #'s that are in the parenthesis().
For the 2nd question, it's either A) Reflexive Property or C) Symmetric Property...
how to find the volume of a sphere
Answer:
V = [tex]\frac{4}{3} \pi r^3[/tex]
Step-by-step explanation:
Final answer:
To find the volume of a sphere, use the formula: Volume = 4/3 (pi) (radius)^3
Explanation:
The volume of a sphere can be calculated using the formula:
Volume = 4/3 (pi) (radius)^3
To find the volume, you need to know the radius of the sphere. Plug in the value for the radius and then evaluate the expression using the order of operations. Finally, multiply the result by 4/3 and pi to find the volume of the sphere.
the soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Answer:
4 people voted for hot dogs
Step-by-step explanation:
20-6-10=4
Answer:
Not sure what your exact question is, but I'll make an assumption that you are asking for the percentages of each statistic. It's going to be:
30% pizza
50% chicken
20% hot dogs
Step-by-step explanation:
Because you have 20 members, to get a total percentage, I divided by 2 to get to 10, which is going to make it easier to determine the percentages.
Next, because you divided the total players by 2, you have to do the same for each of the votes as well. Six becomes three, 10 becomes 5, and the rest (which is four) becomes two.
Now, you need to multiply by 10 to get the exact percentage. 10 becomes 100%, and the same for all the other numbers.
Hope this helps!
2350 meters is how many kilometers
Answer:
Your answer would be 2.35. All you have to do id divided how many meters you have by 1000. Hope it Helped
Step-by-step explanation:
km=m times 1000
5/6 + (-1/2)value of sum
Answer:
it's 1/3
Step-by-step explanation:
5/6+(-1/2)
5/6-1/2
LCM= 6
(5-3)/6
2/6
1/3
Factor of 27x ( exponent of 3) - 125
[tex]\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\27x^3-125=3^3x^3-5^3=(3x)^3-5^3=(3x-5)[(3x)^2+(3x)(5)+5^2]\\\\=\boxed{(3x-5)(9x^2+15x+25)}[/tex]
James has a model helicopter. The model is 8 inches long and 7 inches wide. The actual helicopter is 56 inches long. What is the helicopters actual width, if we assume the models proportions are accurate?
A: 40 inches
B: 49 inches
C: 56 inches
D: 60 inches
Answer:
49 inches
Step-by-step explanation:
Write and solve an equation of ratios, as follows:
7 inches x
-------------- = -----------------
8 inches 56 inches
Then (8 ")x = (7 ")(56 "), and
x = 392/8 inches = 49 inches.
The actual width of the helicopter is 49 inches.
The actual width is found to be 49 inches, which corresponds to answer choice B.
The question is asking us to determine the actual width of a helicopter given its scale model dimensions and the actual length. To solve the problem, we use the concept of ratios or proportions. The scale model is 8 inches long and 7 inches wide, and the actual helicopter is 56 inches long.
We set up a proportion to find the actual width:
Model length : Actual length = Model width : Actual width8 inches : 56 inches = 7 inches : x inchesTo solve for x, we cross multiply:
8 * x = 56 * 7
x = (56 * 7) / 8
x = 392 / 8
x = 49 inches
Therefore, the correct answer is B: 49 inches, which is the actual width of the real helicopter.
Simplify the expression. 3x2 + x − x2 − 2x
A. 2x
B. 2x2 − x
C. 3x2 − 2x
D. 4x2 − 3x
Answer:
B. 2x^2 − x
Step-by-step explanation:
3x^2 + x − x^2 − 2x
We need to combine like terms
3x^2 -x^2+ x − 2x
2x^2 -x
The expression 3x² + x - x² - 2x simplifies to 2x² - x, which is Choice B.
To simplify the expression 3x² + x - x² - 2x, you can combine like terms. The equation has two terms involving x squared (x²) and two terms involving x to the first power.
Combine the x² terms: 3x² - x² = 2x².
Next, combine the x terms: x - 2x = -x.
Putting them together, the simplified expression is 2x² - x.
Therefore, the answer is Choice B: 2x² - x. This step-by-step process demonstrates the importance of combining like terms and simplifying expressions to arrive at the correct solution.
Find the slope of the line passing through the pair of points. (7, 6) and (−7, −6)
A. −17
B. 67
C. −1
D. −57
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (7, 6) and (-7, -6). Substitute:
[tex]m=\dfrac{-6-6}{-7-7}=\dfrac{-12}{-14}=\dfrac{12}{14}=\dfrac{6}{7}[/tex]
Answer: B. 6/7Final answer:
The slope of the line passing through the points (7, 6) and (-7, -6) is 6/7, which is not reflected in the provided options, hinting at an error in the question or the answer choices.
Explanation:
To find the slope of the line passing through the points (7, 6) and (-7, -6), we use the slope formula, which is:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula gives us:
m = (-6 - 6) / (-7 - 7)
Which simplifies to:
m = (-12) / (-14)
And further simplifies to:
m = 6/7
However, this result is not among the provided options, which suggests there may have been an error in the question or in the options given. The correct slope calculated from the provided points is 6/7, not any of the options presented (A, B, C, D).
the sum of 9 and twice a number use the variable n to represent the unknown number
Answer:
9 + 2n =
Step-by-step explanation:
9 + 2n =
Answer:
It would be 9+2n.
Step-by-step explanation:
Sinve you have not given us an equation, twice a number can also be reresented as 2n. Since 9 is the constant, you can say 9+2n.
(80 Points)Explain why any of the four operations (+-x/)placed between the two terms 5 and-3/(radical sign) 8 will result in an irrational number.
5±x[tex]\frac{-3}{√8}[/tex] is an irrational number because there's a radical in the denominator. It wouldn't result in a whole number. It would have to be rationalized or smth
Math help quickkk! How many cupcakes can the baker decorate per minute
Answer:
It would be 1 and 2/5 or 1.4 per minute.
Step-by-step explanation:
A 3-ounce package of pistachios cost $5.99 what is the unit rate???!
Answer: 1.996666666666667
Step-by-step explanation:
3ounces divided by 5.99
Answer:If you round 5.99 it would be 6.00 and then dived 3 and 6.00 its going to be 1.5 because you have to split it up
Step-by-step explanation:
what is 3/8+2/5 equal if someone answers can you guys please explain it to me please
Answer:
31/40
Step-by-step explanation:
LCD = 40
Multiplying numerators and denominators to get the LCD in all fraction denominators
Then rewriting the equation with the equivalent fractions
With like denominators we can operate on just the numerators
Answer:
31/40
Step-by-step explanation:
3/8+2/5
First make them both have same denominator:
3/8 8 x 5= 40 3 x 5=15/40
2/5 5 x 8=40 2x8=16 16/40
15/40+16/40=31/40
20 Points!! Plzz Help!!! Will give brainliest!!! Hurry Plzz Need Help ASAP!!!
If l || m, m<7 = 2x and m<2 = x, then what is the measure of angle 2?
A. 30°
B. 60°
C. 90°
D. 120°
Answer:
60
Step-by-step explanation:
anwser: B.
see explanation
The number of fruit tarts that a baker makes each day is 40% of the total number of desserts she makes. On Monday, the baker makes 90 desserts total. What is the number of fruit tarts the baker makes on Monday?
Question 1 options:
36
50
54
225
Answer:
36 fruit tarts
Step-by-step explanation:
90 x .40 = 36
An investor invested a total of $3 comma 500 in two mutual funds. One fund earned a 4% profit while the other earned a 2% profit. If the investor's total profit was $110, how much was invested in each mutual fund
Answer:
$2000 invested in first fund
$1500 invested in second fund
Step-by-step explanation:
An investor invested a total of $3,500 in two mutual funds.
Let x be the amount invested in first fund
first fund earned a 4% profit (4%= 0.04)
So interest is 0.04x for first fund
Let x be the amount invested in first fund
first fund earned a 4% profit (4%= 0.04)
So interest is 0.04x for first fund
Let y be the amount invested in second fund
second fund earned a =2% profit (2%= 0.02)
So interest is 0.02y for second fund
An investor invested a total of $3,500 in two mutual funds.
So x+y = 3500----> equation 1
y= 3500-x
the investor's total profit was $110
0.04x + 0.02y = 110----> equation 2
Plug in 3500 -x for y
0.04x + 0.02(3500-x) = 110
0.04x + 70 - 0.02x = 110
0.02x + 70 = 110
Subtract 70 onboth sides
0.02x = 40
Divide both sides by 0.02
x= 2000
y= 3500-x
so y= 3500 - 2000 = 1500
$2000 invested in first fund
$1500 invested in second fund
Need help with 21-22, 27-34 plz
Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for $1.10/lb. How many pounds of lollipops are in the mixture?
Could I have an equation for the problem.
Thank you so Much!
Answer:
Twenty Pounds
Step-by-step explanation:
Equation #1:
30lbs x Mix Price = (Lollipop Lbs x 0.95) + (Caramel Lbs X 1.10)
Equation #2:
Lollipops Lbs + Caramel Lbs = 30 Lbs
Rearrange expressions to solve for different variables
EQ1: Caramel Lbs = (30 - .95 Lollipop Lbs)/ 1.10 NOTE: (mix price = 1.00)
EQ2: Lollipop Lbs = 30 - Caramel Lbs
Substitute formula 1 into formula 2
Lollipop Lbs = 30 - [(30 - .95 Lollipop Lbs)/1.10]
Distribute divisor
Lollipop Lbs = 30 - 27.2727 + .8636 Lollipop Lbs
Collect terms
Lollipop Lbs = 2.7273 + .8636 Lollipop Lbs
Remove .8336 Lollipops from both sides of the equation
.1364 Lollipop Lbs = 2.7273
Divide both sides by .1364 (Answer is 19.9949 which rounds to 20)
Lollipop Lbs = 20
PROOF:
30 = (20 x 0.95) + (10 x 1.10)
30 = 19 + 11
30 = 30 TRUE!
To determine the number of pounds of lollipops in the mixture, we can set up an equation with the total weight of the mixture and the weight of the lollipops. Solving the equation, we find that there are 15 pounds of lollipops in the mixture.
Explanation:
To solve this problem, we can set up an equation using the given information.
Let x represent the number of pounds of lollipops in the mixture.
Since Rachel has a total of 30 pounds of the mixture, we can write the equation: x + (30 - x) = 30
Simplifying the equation, we have: 2x = 30
Dividing both sides by 2, we find that x = 15.
Therefore, there are 15 pounds of lollipops in the mixture.
Learn more about Lollipops here:https://brainly.com/question/17179286
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Which of the following could be the equation of the function below?
Answer:
[tex]y=-2cos (2(x+\pi ))-1[/tex]
Step-by-step explanation:
From the graph, we can see that y = -3 when x = 0.
So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.
1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1 = 3
2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1
3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3
Therefore, the equation of this graph is y = -2 cos (2(x + pi)) - 1.
IN THE MIDDLE OF THE TEST PLEASE!!
What is the solution to this system of equations? y=3xy=x+2
Y = 3x
Y = x+2
set the two y's equal to each other
3x=x+2
Isolate the x
2x=2
divide
ANSWER: x=1 y=3 or (1,3)
Answer:the anwser is (3,9)
Step-by-step explanation:I orgainly thought 1,3