By setting up a system of equations based on the given information, we find that Brenda sewed 12 buttons on 28 dresses.
Explanation:Since there are 90 dresses in all, Brenda would have sewed 8 buttons on some and 12 buttons on the remaining. We can set up a system of equations to solve this. Let's say the number of dresses that have 8 buttons is 'x' and the number of dresses with 12 buttons is 'y'. Hence, we have two equations:
x + y = 90 (which is the total number of dresses)8x + 12y = 784 (which is the total number of buttons)From the first equation, we get x = 90 - y. Substituting this into the second equation, we have 8*(90 - y) + 12y = 784. Solving this yields, y = 28. Therefore, Brenda sewed 12 buttons on 28 dresses.
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A box contains 5 red marbles and 7 green marbles. Find the probability of drawing 2 red marbles.
1. a) with replacement
2. b) without replacement
Answer:
1) 25/144 or 0.1736
2) 5/33 or 0.1515
Step-by-step explanation:
Total marbles: 5 + 7 = 12
1) 5/12 × 5/12
25/144
0.173611111
2) 5/12 × 4/11
5/33
0.151515151515
Answer:
1. 25/144
2. 5/33
Step-by-step explanation:
1. There are a total of 12 marbles. The probability of drawing the first marble red is: 5/12. Since we replace the marble, when we draw the second marble, the probability will also be 5/12. So we multiply them together and get: 25/144.
2. Again the probability of drawing the first marble red is 5/12. However, this time we're not replacing. This means that there are 12 - 1 = 11 remaining marbles and 5 - 1 = 4 remaining red marbles. Then the probability of choosing a second red marble is: 4/11. Multiply these two together: (5/12) * (4/11) = 20/132 = 5/33
Hope this helps!
Multiply and simplify the following complex numbers: (1 + 2i) x (1 - 4i)
Answer:
9-2i
Step-by-step explanation:
(1 + 2i) * (1 - 4i)
(1*1)-(1*4i)+(2i*1)-(2i)*(4i)
(1)-(4i)+(2i)-(8i^2)
i^2 = -1
1-4i+2i+8
1-2i+8
9-2i
The multiplication and simplification of the complex numbers (1 + 2i) x (1 - 4i) results in 9 - 2i.
Explanation:To multiply and simplify the complex numbers (1 + 2i) and (1 - 4i), we must use the distributive property, just like in normal algebra. We get (1*1) + (1*-4i) + (2i*1) + (2i*-4i), which is 1 - 4i + 2i - 8i². But remember, in complex numbers, i² equals -1, so it simplifies further to 1 - 2i -8(-1), or 1 - 2i + 8, and finally, 9 - 2i which is our final, simplified result.
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What is the value of the rational expression x-2x2-3/4x2-12 when x = 3?
-1/4
0
1/4
undefined
Answer:
(-135)/4
Step-by-step explanation:
Evaluate -(3 x^2)/4 - 2 x^2 + x - 12 where x = 3:
-(3 x^2)/4 - 2 x^2 + x - 12 = 3 - 2×3^2 - 3/4×3^2 - 12
3^2 = 9:
3 - 29 - 3/4×3^2 - 12
3^2 = 9:
3 - 2×9 - 3/4×9 - 12
-2×9 = -18:
3 + -18 - 3/4×9 - 12
-3×9 = -27:
3 - 18 + (-27)/4 - 12
Put 3 - 18 - 27/4 - 12 over the common denominator 4. 3 - 18 - 27/4 - 12 = (4×3)/4 + (4 (-18))/4 - 27/4 + (4 (-12))/4:
(4×3)/4 - (18×4)/4 - 27/4 - (12×4)/4
4×3 = 12:
12/4 - (18×4)/4 - 27/4 - (12×4)/4
4 (-18) = -72:
12/4 + (-72)/4 - 27/4 - (12×4)/4
4 (-12) = -48:
12/4 - 72/4 - 27/4 + (-48)/4
12/4 - 72/4 - 27/4 - 48/4 = (12 - 72 - 27 - 48)/4:
(12 - 72 - 27 - 48)/4
12 - 72 - 27 - 48 = 12 - (72 + 27 + 48):
(12 - (72 + 27 + 48))/4
| 1 |
| 7 | 2
| 4 | 8
+ | 2 | 7
1 | 4 | 7:
(12 - 147)/4
12 - 147 = -(147 - 12):
(-(147 - 12))/4
| 1 | 4 | 7
- | | 1 | 2
| 1 | 3 | 5:
Answer: (-135)/4
Imagine we found a strong positive correlation between worry and sleep disturbances and we hypothesized that drinking caffeine before going to bed would exacerbate this relationship. What type of analysis could we conduct to test this hypothesis?a. Moderationb. Mediationc. ANCOVAd. Two-way ANOVA
Answer:
The correct option is;
a. Moderation
Step-by-step explanation:
Here we have that the analysis is to check the hypothesis that drinking caffeine would exacerbate the effect of sleep disturbance caused worry is a form of moderator analysis.
A moderator analysis is one in which we attempt to determine if the relationship between two investigated variables is dependent on the magnitude or presence of a third variable. We refer to the third variable as the moderator or moderator variable.
What is this???): pls help
Answer:
sin D= 12/15
sin E= 9/15
cos D=9/15
Step-by-step explanation:
Use SOH CAH TOA
Sine= opposite/hypotenuse
Cosine= adjacent/hypotenuse
Tangent= opposite/adjacent
Chef Selena is making her special dish that requires pasta, sauce, and onions. She has 5 1/8 pounds of pasta, 6 pounds of sauce, and 4 7/8 pounds of onions. How many servings of her dish can she make if each serving is 1/2 pound? Which two equations are needed to solve the problem?
Answer:
[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]
Step-by-step explanation:
The Weight of Ingredients to be used by Chef Selena are:
[tex]5\frac{1}{8}[/tex] pounds of pasta, 6 pounds of sauce; and [tex]4\frac{7}{8}[/tex] pounds of onions.Total Weight of Food Made, x
[tex]=5\frac{1}{8}+6+4\frac{7}{8}\\=5+6+4+\frac{1}{8}+\frac{7}{8}\\=16 \: Pounds[/tex]
Since each serving is [tex]\frac{1}{2} Pounds[/tex]
Number of Servings of her dish, y
[tex]16 \div \frac{1}{2}\\ =32 \: Servings[/tex]
The two equations needed to solve the problem are therefore:
[tex]\text{Total Weight of Food Made}, x=5\frac{1}{8}+6+4\frac{7}{8}\\\text{Number of Servings}, y=x \div \frac{1}{2}[/tex]
Jake ran 145 meters before lunch and 389 meters after lunch. How many kilometers did Jake run in all? 0.00534 km 0.0534 km 0.534 km 5.34 km
Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.
Step-by-step explanation:
The given is,
Jake ran 145 meters before lunch.
389 meters after lunch.
Step:1
Total distance ran by Jake,
Total distance = Jake run before lunch + Jake run after lunch...(1)
Where,
Jake run before lunch = 145 meters
Jake run after lunch = 389 meters
Equation (1) becomes,
Total distance = 145 + 389
= 534
Total distance = 534 meters
Step:2
1 kilometer = 1000 meters
Total distance ran by Jake = 534 meters
= [tex]\frac{534}{1000}[/tex] kilometers
= 0.534
Total distance ran by Jake = 0.534 km
Result:
Jake ran 0.534 km in all, if he ran 145 meters before lunch and 389 meters after lunch.
Answer:
0.534
Step-by-step explanation:
I did the work
The height of a trapezoid is 8 in. And its area is 64 in2. One base of the trapezoid is 6 inches longer than the other base. What are the lengths of the bases?
Answer:
5 and 11
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)*h
We know the height is 8 and the area is 64.
Let one of the bases is b and the other is b+6
64 = 1/2 (b+ b+6) *8
Combine like terms
64 = 4 (2b+6)
Divide each side by 4
64/4 = 4/4 *(2b+6)
16 = 2b+6
Subtract 6 from each side
16-6 = 2b+6-6
10 =2b
Divide each side by2
10/2 =2b/2
5=b
The second base is
5+6 =11
Brad can type 1260 words in 1/2 hour. What is Brad’s average typing rate in words per minute?
Brad average typing rate in words per minute is 21
1260 divided by 60 = 21
(In case you meant 30 minutes)
1260 divided by 30 = 42
5/7 = p + 4/7
p =
Solve the equation.
Step-by-step explanation:
p=5/7-4/7
7p=1
p=1/7
hope it helps
Answer:
Step-by-step explanation:
The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed. Given this information, the approximate percentage of the population with an IQ greater than 130 is closest to _________.
Answer:
2.28% is the approximate percentage of the population with an IQ greater than 130.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 15
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(IQ greater than 130)
[tex]P( x > 130) = P( z > \displaystyle\frac{130 - 100}{15}) = P(z > 2)[/tex]
[tex]= 1 - P(z \leq 2)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 130) = 1 - 0.9772 = 0.0228 = 2.28\%[/tex]
2.28% is the approximate percentage of the population with an IQ greater than 130.
The approximate percentage of the population with an IQ greater than 130 will be 2.28%.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The mean intelligence quotient (IQ) score is 100, with a standard deviation of 15, and the scores are normally distributed.
Then the approximate percentage of the population with an IQ greater than 130 will be
The value of z-score
z = (130 - 100) / 15
z = 30 / 15
z = 2
Then the probability will be
P(x > 130) = P(z > 2)
P(x > 130) = 1 - P(z < 2)
P(x > 130) = 1 - 0.97725
P(x > 130) = 0.02275
Then the percentage will be
P = 0.02275 x 100
P = 2.275%
P ≅ 2.28%
More about the normal distribution link is given below.
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3. What is x?
E
4x+ 5
H
If the volume of an object is 100cm3 and the density is 4g/cm3. What is the mass of the object in g?
Answer:
400g
Step-by-step explanation:
mass= density × volume
Substitute the given value of density and volume.
Mass of the object
= 4(100)
= 400g
You are building a sandbox for your little sister. You want to make sure that she has 200 cubic ft. Of space to play. Give a possible length, width, and height of the sandbox.
Answer:
10x10x2
Step-by-step explanation:
10 * 10 * 2 = 200
A cylinder has a radius of 1 inch and a height of 1 inch. What is the approximate volume of the cylinder? Round to the nearest hundred. Use 3.14 for pie
Grace had 4 3/8 yards of elastic. She used 1 2/3 yards of the elastic to make bracelets for her friends. How many yards of elastic does she have now?
A. 6 1/24
B. 3 7/24
C. 2 17/24
D. 3 17/24
Answer: D. 3 17/24
Step-by-step explanation:
4 3/8 - 1 2/3
Michael is packing his bags for his vacation. He has 6 unique toy animals, but only 5 fit in his bag. How many different groups of 5 toy animals can he take?
Answer:
6 different groups of toy animals
Step-by-step explanation:
In this question, we are to calculate the number of different groups of toy animals Michael can take.
Since we are selecting, this is clearly a COMBINATION question. Now from the question, we are trying to select 5 toy animals from a group of 6 different animals to fit in the bag
The number of ways we can do this is 6C5 ways
Mathematically, if we have to select a number of r items from a group of n items, the number of ways this can be done is;
nCr = n!/(n-r)!r!
Using the case in the question, we have; 6!/5!(6-5)! = 6!/5!1! = 720/120 = 6 groups
Answer:
6 different groups of toy animals
Step-by-step explanation:
The question above can be solved by applying the Combination technique
Combination technique uses the formula:
nCk = n! /k!(n-k)!
Where in the question above:
n = 6
k = 5
Therefore we have , 6C5
= 6! / 5! (6-5)!
= 6!/ 5!(1!)
6! = 6×5×4×3×2×1
5! = 5×4×3×2×1
Hence,
= (6×5×4×3×2×1) / (5×4×3×2×1)(1)
= 6
Hence, Michael can take 6 different groups of toy animals with him on his vacation.
Calculate the area of the shaded region. Use 3.14 for pi. Round your answer to the nearest hundredth if necessary
Based on the diagram shown above, the area of the shaded region rounded to the nearest hundredth is 1.34 square meter.
In Mathematics and Euclidean Geometry, the area of a square can be calculated by using this formula;
A = [tex]s^2[/tex]
Where:
A is the area of a square.s is the side length of a square.By substituting the given side lengths into the formula, we have;
Area of square, A = 2.5 × 2.5
Area of square, A = 6.25 square meters.
In Mathematics and Geometry, the area of a circle can be calculated by using this formula:
Area of circle = π[tex]r^2[/tex]
Where:
r represents the radius of a circle.
By substituting, we have;
Radius of circle = diameter/2 = 2.5/2
Radius of circle = 1.25 m.
Area of circle = π × [tex]1.25^2[/tex]
Area of circle ≈ 4.91 square meters.
Area of the shaded region = Area of square - Area of circle
Area of the shaded region = 6.25 - 4.91
Area of the shaded region = 1.34 square meter.
The area of the shaded region is Area = 1.34 [tex]m^2[/tex].
To find the area of the shaded region (the area outside the circle but inside the square), we need to calculate the area of the square and the area of the circle, then subtract the area of the circle from the area of the square.
Given:
Side length of the square [tex]\(s = 2.5\)[/tex] meters
Use [tex]\( \pi = 3.14 \)[/tex]
1. Calculate the area of the square:
[tex]\[ \text{Area of the square} = s^2 = 2.5^2 = 6.25 \text{ square meters} \][/tex]
2. Calculate the radius of the circle:
Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square.
[tex]\[ \text{Diameter of the circle} = 2.5 \text{ meters} \][/tex]
[tex]\[ \text{Radius of the circle} = \frac{2.5}{2} = 1.25 \text{ meters} \][/tex]
3. Calculate the area of the circle:
[tex]\[ \text{Area of the circle} = \pi r^2 = 3.14 \times (1.25)^2 \][/tex]
[tex]\[ \text{Area of the circle} = 3.14 \times 1.5625 = 4.90625 \text{ square meters} \][/tex]
4. Calculate the area of the shaded region:
[tex]\[ \text{Area of the shaded region} = \text{Area of the square} - \text{Area of the circle} \][/tex]
[tex]\[ \text{Area of the shaded region} = 6.25 - 4.90625 = 1.34375 \text{ square meters} \][/tex]
Rounded to the nearest hundredth:
[tex]\[\text{Area of the shaded region} \approx 1.34 \text{ square meters}\][/tex]
The complete question is:
Calculate the area of the shaded region. Use 3.14 for pi. Round your answer to the nearest hundredth if necessary.
Area = ____ [tex]m^2[/tex].
Given that the measure of ∠x is 123°, and the measure of ∠y is 51°, find the measure of ∠z. °
Answer:
The measure of angle z is 59°.
Step-by-step explanation:
Final answer:
To find the measure of ∠z when ∠x = 123° and ∠y = 51°, add the angles and subtract the sum from 180°.
Explanation:
Given:
∠x = 123°
∠y = 51°
To find ∠z:
Add ∠x and ∠y: 123° + 51° = 174°
Since the sum of angles in a triangle is 180°, subtract the sum of ∠x and ∠y from 180° to find ∠z: 180° - 174° = 6°
Hence, ∠z = 6°.
There are 100 senators in the 115th Congress. Democrats make up $\frac{46}{100}$ of the senators, and Republicans make up $\frac{13}{25}$ of the senators. The rest are Independents. What fraction of the senators are Democrat or Republican?
Answer: The fraction that makes up Democrats or Republicans is 49/50.
Step-by-step explanation: There are 100 senators in total. We have 46/100 representing the Democrats, and 13/25 representing the Republicans. The number representing the Republicans can be made into an equivalent fraction of the other simply by multiplying both numerator and denominator by 4 (in order to make the denominator the same, that is 100). Hence the fraction of Republicans is 52/100, while the rest are Independents. The independents are
Ind = 100 - (46/100 + 52/100)
Ind = 100 - 98/100
Ind = 2/100
{Total = 46/100 + 52/100 + 2/100}
{Total = 100/100}
However, the fraction of all senators that are Democrats or Republicans is derived as follows;
Dems = 46/100
Reps = 52/100
Total fraction = 46/100 + 52/100
Total fraction = 98/100
Total fraction = 49/50
Final answer:
To find the fraction of senators who are Democrat or Republican, we add the fractions representing Democrats and Republicans. The fraction is $rac{49}{50}$.
Explanation:
To find the fraction of senators who are Democrat or Republican, we need to add the fractions representing Democrats and Republicans. The fraction of senators who are Democrats is $rac{46}{100}$, and the fraction of senators who are Republicans is $rac{13}{25}$.
To add these fractions, we need a common denominator. The least common multiple of 100 and 25 is 100, so we can rewrite the fractions with denominators of 100. $rac{46}{100}$ is equivalent to $rac{46}{100} imes rac{1}{1}$, and $rac{13}{25}$ is equivalent to $rac{13}{25} imes rac{4}{4}$ (since $25 imes 4 = 100$).
Now we can add the fractions: $rac{46}{100} + rac{13}{25} = rac{46}{100} + rac{52}{100} = rac{98}{100}$.
So, $rac{98}{100}$ of the senators are Democrat or Republican, which simplifies to $rac{49}{50}$.
Solve for x in the equation x^2 - 4x-9= 29
I'm guessing 4+-√42 if u can understand it's the last one....
If I am going 70 miles per hour and I am talking to someone for 66 seconds and 513 milliseconds how long would it take for my car to travel with the extra time
Answer:
Car would have traveled [tex]1.283[/tex] miles more with the extra time
Step-by-step explanation:
Given
Speed of the car - [tex]70[/tex] miles per hour
Speed of car in miles per second
[tex]\frac{70}{60* 60}[/tex]
[tex]= 0.0194[/tex] miles per second
Time wasted in talking instead of travelling
[tex]66[/tex] seconds and [tex]513[/tex] milliseconds
Total time wasted in seconds
[tex]66 + \frac{513}{1000} \\66 + 0.513[/tex]
[tex]66.153[/tex] seconds
Distance that would have been traveled in this time instead of talking
[tex]0.0194[/tex] miles per second [tex]* 66.153[/tex] seconds
[tex]= 0.0194 * 66.153[/tex] miles
[tex]= 1.283[/tex] miles
Can someone help me on this
Evaluate each expression
Answer:
a. 32
b. 27
c. 64
d. 36
e. 1/16
f. 1/9
Answer:
a.32
b.27
c.64
d.36
e.1/16
f.1/9
Step-by-step explanation:
Hope it helps.!
What is the area of a circle with a diameter of eight
Answer:
16 pi or approximately 50.24
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
r = d/2 where d is the diameter
r = 8/2 =4
So plugging into the equation for the area
A = pi (4)^2
A = 16pi
Using 3.14 as an approximation for pi
A = 16*3.14 =50.24
Let B1W2 denote the outcome that the first ball drawn is B1 and the second ball drawn is W2. Because the first ball is replaced before the second ball is drawn, the outcomes of the experiment are equally likely. List all 25 possible outcomes of the experiment on a sheet of paper.Consider the event that the first ball that is drawn is blue.
Answer:
[tex]\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\[/tex]
[tex]W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}[/tex]
Step-by-step explanation:
[tex]\text{If an urn contains two blue balls} (denoted \:B_1 \:and \:B_2) \text{and three white balls}[/tex],[tex](denoted \:W_1, W_2, \:and\: W_3)[/tex]
If One ball is drawn, its color is recorded, and it is replaced in the urn. Then another ball is drawn and its color is recorded.
The 25 Possible outcomes of this experiment are listed below:
[tex]\{B_1B_1, B_1B_2, B_1W_1, B_1W_2, B_1W_3, \\B_2B_1, B_2B_2, B_2W_1, B_2W_2, B_2W_3, \\[/tex]
[tex]W_1B_1,W_1B_2, W_1W_1, W_1W_2, W_1W_3, \\W_2B_1, W_2B_2, W_2W_1,W_2W_2, W_2W_3, \\W_3B_1, W_3B_2, W_3W_1, W_3W_2, W_3W_3\}[/tex]
The tree diagram of this event is also attached.
If you reflect point A (3, 4) over
the y-axis, what is the reflected
point?
The rule for reflecting a point over the y-axis is this:
(x, y) ---> (-x, y)
The x term becomes the opposite and the y term stays the same
(3, 4) ---> (-3, 4)
Hope this helped! Let me know if you have any further questions!
~Just a girl in love with Shawn Mendes
Jose is working two summer jobs, making $10 per hour washing cars and $9 per hour walking dogs. Last week Jose worked a total of 13 hours and earned a total of $122. Write a system of equations that could be used to determine the number of hours Jose worked washing cars last week and the number of hours he worked walking dogs last week. Define the variables that you use to write the system.
Answer:
x+y =13
10x + 9y =122
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations:
The sum of the hours he worked washing cars (x) and the hours he worked walking dogs(y) will be equal to the total hours worked (13)
x+y =13For the second equation the product of the number of hours he worked washing cars(x) and the price per hour ($10) plus the product of the number of hours he worked walking dogs (y) and the price per hour ($9) will be equal to the total amount earned (122)-
10x + 9y =122So, the system of equations is:
x+y =13 10x + 9y =122Where:
x: number of hours Jose worked washing cars
y: number of hours Jose worked walking dogs
Based on the information given, the equation will be:
x + y = 1310x + 9y = 122Based on the information given, the sum of the hours he worked washing cars and the hours he worked walking dogs will be equal to the total hours worked. Thia can be represented by:
x + y = 13
On the other hand, the product of the number of hours he worked washing cars and the price per hour plus the product of the number of hours he worked walking dogs and the price per hour can be represented with the equation:
10x + 9y = 122
In conclusion, the equation will be x + y = 13 and 10x + 9y = 122.
Learn more about equations on:
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On Friday, 112 grocery shoppers bought a candy bar from the checkout line and 588 grocery shoppers did not. What percentage of shoppers did NOT buy a candy bar?
Answer: 84%
Step-by-step explanation:
112 grocery shoppers bought a candy bar and 588 grocery shoppers did not.
Number of grocery shoppers that bought candy bar = 112
Number of grocery shoppers that did not buy candy bar= 588
Total number of grocery shoppers= 112+588 = 700
Percentage of shoppers did not buy a candy bar= 588/700 × 100
= 0.84 × 100
= 84%
Answer:
0.84 = 84%
Step-by-step explanation:
First we need to find the total number of grocery shoppers.
If 112 bought a candy bar and 588 did not, the total number of grocery shoppers is:
588 + 112 = 700
Now, to calculate the percentage of grocery shoppers that didn't buy a candy bar, we make a division between the number of grocery shoppers that didn't buy a candy bar and the total number of grocery shoppers:
588 / 700 = 0.84 = 84%
Jose Has scored 28,24,26,27,and 21 Points in his five basketball game so far. How many points does he need to score in his next game so that his average mean is 25 points per game
Answer:
The correct answer is 24.
Step-by-step explanation:
Jose wants to have an average mean of 25 points per game in his 6 basket ball matches.
Total points Jose plans to achieve in 6 games is 25 × 6 = 150.
Points score by him in the first five matches are 28, 24, 26, 27 and 21.
Total points in 5 matches is 126.
Thus the points he need to score in his next game to have an average mean of 25 is given by 150 - 126 = 24.