Solution:
Given that,
Dan, Angad & David share some money in the ratio 1 : 1 : 3
Let the share of Dan be 1x
Let the share of Angad be 1x
Let the share of David be 3x
In total, Dan and David receive £52
Therefore,
1x + 3x = 52
4x = 52
x = 13
Therefore,
share of angad = 1x = 13
Thus share of Angad is £ 13
Solve the following equation
sin¢=cos(¢+20°)
Step-by-step explanation:
[tex] \sin \: \phi = \cos( \phi + 20 \degree) \\ \\ \therefore \: \cos (90 \degree - \phi )= \cos( \phi + 20 \degree) \\ \\ \therefore \: 90 \degree - \phi = \phi + 20 \degree \\ \\ \therefore \: 90 \degree - 20 \degree = \phi +\phi \\ \\ \therefore \: 70 \degree = 2\phi \\ \\ \therefore \: \phi = \frac{70 \degree}{2} \\ \\ \huge \red { \boxed{ \therefore \: \phi = 35 \degree}}[/tex]
Which statements are true about the expression 8 (a + 7)? Check all that apply.
1.To simplify, distribute a to 8 and to 7.
2.8(a) can be rewritten as 8a.
3.8 (a + 7) can be rewritten as 8 (a) + 8 (7).
4.8 (a + 7) can be rewritten as 8 (a) + (7).
5.An equivalent expression is 15a.
6.An equivalent expression is 8 a + 7
7.An equivalent expression is 8 a + 56
Answer:
Option 3)
8(a + 7) can be rewritten as 8(a) + 8(7).
Option 7)
An equivalent expression is 8a + 56
Step-by-step explanation:
We are given the following expression:
[tex]8 (a + 7)[/tex]
We can simplify the expression by distributing 8 over (a+7).
Distributive property:
[tex]a(b+c)\\=(a\times b) + (a\times c)\\=a(b) + a(c)\\=ab + ac[/tex]
Simplifying the expression, we get,
[tex]8(a+7)\\=(8\times a)+(8\times 7)\\=8a + 56[/tex]
Thus, the correct options are:
Option 3)
8(a + 7) can be rewritten as 8(a) + 8(7).
Option 7)
An equivalent expression is 8a + 56
The true statements about the expression 8(a+7) are 2, 3 and 7.
When evaluating the expression 8(a+7), several steps can be taken to rewrite or simplify it. Here's a closer look at the provided statements:
Statement 1 suggests to distribute 'a' to 8 and to 7, which is incorrect. The correct procedure is to distribute the 8 to both 'a' and the 7.
Statement 2 correctly suggests that 8(a) can be rewritten as 8a.
Statement 3 is true, as 8(a+7) can be rewritten following the distributive property as 8(a)+8(7), which simplifies to 8a+56.
Statement 4 is incorrect because it omits the distribution of 8 over both terms within the parentheses.
Statement 5 is incorrect as there is no reason to believe that 8(a+7) simplifies to 15a without any additional information.
Statement 6 is incorrect as it implies that the 8 is only multiplied by 'a' and not by the 7.
Statement 7 is correct because the expression 8(a+7) is correctly expanded to 8a+56.
How do you write -9 is -16 as an equation
Answer:
Replace "is" with an equal sign.
Step-by-step explanation:
It looks like you want the equation ...
-9 = -16
which makes no sense at all. Perhaps you intend ...
-g = -16
What are the solutions? Check all of the boxes
that apply.
2x2 - 16x + 34 = x2 - 6x + 10
Answer:
4 and 6
:)
EDGE 2020
Answer:
B) 4
C) 6
Step-by-step explanation:
PLEASE HELP ASAP
Thirty-two people entered the room. One-half of them decided to stay and listen to the speaker. Of those who stayed to listen, three-quarters were bored. There were
people who stayed and were not bored.
Final answer:
The question requires calculating the number of people who stayed and were not bored out of a total of 32 people.
Explanation:
The question involves calculating the number of people who stayed and were not bored out of 32 people.
Half of 32 people stayed: 32 ÷ 2 = 16 stayed.Of those who stayed, three-quarters were bored: 16 x 3/4 = 12 were bored.The number who stayed and were not bored: 16 - 12 = 4 people.Therefore, the number of people who were not bored were 4 people.
NEED HELP URGENTLY ......................................................
I assumed that the unit of measure is ft.
Front+back:
S1=2×(4×3.5/2)=4×3.5=14ft²
2 sides+base:
S2=3×(9×4)=9×12=108ft²
Total area: 14+108=122ft²
Can someone please help me and also explain it because I want to understand it.
Answer:
89.10
Step-by-step explanation:
To find the volume (how much soil can fit) you do Length x Width x Height in this case it is 4 x 9 x 3
4 x 9 x 3 = 108
Now you have to divide the volume by two because you only want to fill half the box.
108/2=54
Now you multiple the volume by the price to figure out how much soil will cost
54 x 1.65 = 89.1
It will cost $89.10
Heyo! I hope your day is going well! I hope I can help you understand this a bit better!
First things first we have to figure out the total volume of the flower box. To do this we do a simple multiplication problem, 3*4*9, or length*width*height. 3*4 is 12, and then 12*9 is 108. So our total volume for the flower box is 108 cubic feet.
Lucy only wants to fill half of her flower box, so we are going to go ahead and divide our total volume, 108 cubic feet, by 2. Our answer here is 54 cubic feet.
The soil Lucy wants to buy is 1.65 for each cubic foot, meaning we should multiply 1.65 and 54.Our final answer is 89.1!
Which experssions are equivalent to 5(1/3x+7)-3(1/2x-4)?
A psychology professor assigns letter grades on a test according to the following scheme.
A: Top 8% of scores
B: Scores below the top 8% and above the bottom 61%
C: Scores below the top 39% and above the bottom 16%
D: Scores below the top 84% and above the bottom 8%
F: Bottom 8% of scores
Scores on the test are normally distributed with a mean of 65.4 and a standard deviation of 9.7. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
The numerical limits for a D grade in psychology can be calculated using the Z-score formula. The cutoff scores are below the top 84% and above the bottom 8%. Using the mean of 65.4 and the standard deviation of 9.7, the numerical limits for a D grade are 52 to 79.
Explanation:To find the numerical limits for a D grade, we need to determine the cutoff scores. According to the given scheme, a D grade corresponds to scores below the top 84% and above the bottom 8%. To calculate these cutoff scores, we can use the Z-score formula. The Z-score is calculated as the difference between a score and the mean, divided by the standard deviation. Using the Z-score table, we can find the Z-scores corresponding to the top 8% and the bottom 8%. Finally, we can use the Z-score formula to find the corresponding scores for those Z-scores.
Given that the mean is 65.4 and the standard deviation is 9.7, we can calculate the Z-scores:
Z-score for the top 8% = 1.405
Z-score for the bottom 8% = -1.405
Using the Z-score formula, where X is the score, the mean is 65.4, and the standard deviation is 9.7:
X = Z * standard deviation + mean
For the top 8%:
X = 1.405 * 9.7 + 65.4 = 79
For the bottom 8%:
X = -1.405 * 9.7 + 65.4 = 52
Therefore, the numerical limits for a D grade are 52 to 79 (rounded to the nearest whole number).
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Please help me let me know how you got the answer
Area of building is [tex]3,84,000m^3[/tex] .
Step-by-step explanation:
Here we have , a figure in given below picture where we have to find volume of this office building , Let's find out:
If we look closely we see that it's basically cuboid with dimensions 50 m by 110 m by 70 m . But there's one small cuboid sliced off from this cuboid with dimensions 50 m by 10 m by (110-90) m i.e. 50 m by 10 m by 20 m .
Area of building = Area of larger cuboid - Area of smaller cuboid
Area of cuboid = [tex]length(width)(breadth)[/tex]
⇒ Area of building = Area of larger cuboid - Area of smaller cuboid
⇒ [tex]Area = (50(110)(70))m^3 - (50(10)(20))m^3[/tex]
⇒ [tex]Area = 3,85,000m^3 - 10,000m^3[/tex]
⇒ [tex]Area = 3,84,000m^3[/tex]
Therefore, Area of building is [tex]3,84,000m^3[/tex] .
smoothie sales are on fire. the price is $3 for an adult and $1 for children. if 260 smoothies were sold for a total of 675.00 how many adults purchased smoothies? how many children?
Answer:
207.5 adult52.5 childrenStep-by-step explanation:
If "a" represents the number of adult smoothies sold, then 260-a is the number of smoothies sold to children. The total revenue is ...
3a +1(260-a) = 675
2a +260 = 675 . . . . . . eliminate parentheses
a + 130 = 337.5 . . . . . . divide by 2
a = 207.5 . . . . . . . . smoothies sold to adults
260-a = 52.5 . . . . . smoothies sold to children
_____
For the given numbers, this is the way it works out. The "half" values suggest there is a typo somewhere, possibly in the curriculum material. Talk to your teacher about this one.
Rationalise the denominator of 1+√2/√2
Answer:((√2) + 2)/2
Step-by-step explanation:
(1+√2)/(√2) x ((√2)/(√2))
(√2(1+√2))/2
((√2)+2)/2
2z+5=5+2z is it commutative property or distributive ?!
Answer:
Commutative property: The formula for this property is a + b = b + a. For example, adding 1 + 2 or 2 + 1 will give us the same answer according to the commutative property of addition.
The price of a pair of earrings is $22 but Priya buys them on sale for $13.20.
By how much was the price discounted?
What was the percentage of the discount?
Solution
Answer:
$8.8040%Step-by-step explanation:
The amount of the discount is the difference between the original price and the discounted price. That was ...
$22.00 -13.20 = $8.80
The percentage of the discount is the ratio of the amount of the discount to the original price. That was ...
8.80/22.00 × 100% = 40%
The price was discounted $8.80. That was a 40% discount.
Final answer:
The price of the earrings was discounted by $8.80 or 40%.
Explanation:
To find the amount by which the price was discounted, subtract the sale price ($13.20) from the original price ($22):
Discount = Original Price - Sale Price
Discount = $22 - $13.20 = $8.80
The percentage of the discount can be found by dividing the discount by the original price and multiplying by 100:
Percentage of Discount = (Discount / Original Price) * 100
Percentage of Discount = ($8.80 / $22) * 100 = 40%
Write the equation of the ellipse that has a center at
(-2, – 6), a vertex at (-8, – 6), and a covertex at
(-2, -3)
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]
Final answer:
The equation of the ellipse is (x+2)²/36 + (y+6)²/9 = 1, where the center is at (-2, -6), the vertex is at (-8, -6), and the covertex is at (-2, -3).
Explanation:
The equation of an ellipse with a center at (-2, -6), a vertex at (-8, -6), and a covertex at (-2, -3) can be determined using the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the distance from the center to a vertex along the major axis, and b is the distance from the center to a covertex along the minor axis. In this case, the major axis is horizontal because the vertex has the same y-coordinate as the center. Thus, a = 6 (the distance from the center to the vertex) and b = 3 (the distance from the center to the covertex).
The equation becomes: (x+2)²/6² + (y+6)²/3² = 1. Simplified, this is (x+2)²/36 + (y+6)²/9 = 1.
henry rolls 2 number cubes numbered 1 through 6 while playing his favorite board game. he will get a second turn if he rolls a sum that is an even number less than 10. what are henry’s chances of getting a second turn when he rolls the number cubes
Henry has 13 chances to get a second turn.
Step-by-step explanation:
When two number cubes numbered from 1 to 6 are rolled, the number of possible outcomes are 36.
The 36 possible outcomes are as follows :
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
It is given that, Henry gets the second turn if he rolls a sum that is an even number less than 10.
Therefore, the even numbers less than 10 are {2,4,6,8}.
Check for the sum of outcomes that gives the result of even number less than 10.
Sum of (1,1) (1,3) (1,5) gives 2,4,6 which are even numbers less than 10 ⇒ 3 chances.Sum of (2,2) (2,4) (2,6) gives 4,6,8 which are even numbers less than 10 ⇒ 3 chances.Sum of (3,3) (3,5) gives 6 and 8 which are even numbers less than 10 ⇒ 2 chances.Sum of (4,2) (4,4) gives 6 and 8 which are even numbers less than 10 ⇒ 2 chances.Sum of (5,1) (5,3) gives 6 and 8 which are even numbers less than 10 ⇒ 2 chances.Sum of (6,2) gives 8 which is a even number less than 10 ⇒ 1 chance.The total number of chances to get second turn = 3+3+2+2+2+1 = 13 chances.
Therefore, Henry has 13 chances to get a second turn.
Which expressions are equivalent to R16? Check all that apply.
0 (60)*
(80) •
blouse
(02)0
0 (89)16
Option C: [tex](6^{-4})^{-4}[/tex]
Option D: [tex](6^{-2})^{-8}[/tex]
Option F: [tex](6^8)^2[/tex]
Solution:
Given expression: [tex]6^{16}[/tex]
To find which expression is equivalent to the given expression.
Let us solve this using exponent rule: [tex]\left(a^{b}\right)^{c}=a^{b c}[/tex]
Option A: [tex](6^{0})^{16}[/tex]
[tex](6^{0})^{16}=6^{0 \times 16}= 6^0[/tex]
It is not equivalent expression.
Option B: [tex](6^8)^8[/tex]
[tex](6^{8})^{8}=6^{8 \times 8}= 6^{64}[/tex]
It is not equivalent expression.
Option C: [tex](6^{-4})^{-4}[/tex]
[tex](6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Option D: [tex](6^{-2})^{-8}[/tex]
[tex](6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Option E: [tex](6^{-1})^{16}[/tex]
[tex](6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}[/tex]
It is not equivalent expression.
Option F: [tex](6^8)^2[/tex]
[tex](6^{8})^{2}=6^{8 \times 2}= 6^{16}[/tex]
It is equivalent expression for the given expression.
Hence [tex](6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2[/tex] are the equivalent expressions.
Option C, Option D and Option F are correct answers.
PLEASE HELP QUICK!!!!! WORTH 50 POINTS!!!!!!! Explain how to solve the equation. StartFraction c over 6 EndFraction = 9
Answer:
Solve by undoing the division by multiplying by 6 on both sides of the equation. The solution is c = 54. Check the solution by substituting 54 for the variable in the original equation and then simplify. 9 = 9 is true, so 54 is the solution.
Step-by-step explanation:
The value of c is 54.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
c/6 = 9
Solve for c.
c/6 = 9
Multiply 6 on both sides.
c = 9 x 6
c = 54
Thus,
c is 54.
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Anna has a rectangular that is 33 inches and 75 inches. Find the perímeter of the rectangular in yards
Answer:
6 yards
Step-by-step explanation:
Perimeter of a rectangle: 2a + 2b
2(33) + 2(75)
66 + 150
216 inches
216/12 gives us feet
18/3 gives us yards
6 yards
Answer: 6 yards
Is (-2,-6) a solution of y < 7x +8?
Choose 1 answer:
A)Yes
B)NO
Answer:
No
Step-by-step explanation:
-6 < 7(-2) + 8
-6 < -14+8
-6 < -6
False statement
[tex]\large\text{Hey there!}[/tex]
[tex]\mathsf{y< 7x+8}[/tex]
[tex]\large\text{In order for you to see if its true or false just plug in the x and y}\\\large\text{value in your equation. Here's what I meant}\downarrow[/tex]
[tex]\mathsf{-6<7(-2)+8}\\\mathsf{7(-2)=-14}\\\mathsf{-14+8=-6}\\\mathsf{-6\neq-6}[/tex]
[tex]\boxed{\boxed{\large\text{\bf{The answer is: \boxed{\mathsf{\bf{}No,\ because\ -6\ is\ NOT\ less\ than\ -6}}}}}}\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dag\dfrac{\frak{LoveYourselfFirst}}{:)}\notlessth[/tex]
What is the value of x in this equation ? 5x -14 = 8x + 4
in a right triangle, the 58cm hypotenuse makes a 51 angle with one of the legs. rounded to two decimals places, how long is that leg?
Answer:
36.50
To two decimal places
Step-by-step explanation:
The hypothenuse side in a right angle triangle has 58cm. While the angle touching one of its leg is 51°. How long is that leg.
From the right angled triangle, the size of the leg touching the hypothenuse is the adjacent side of the triangle, hence in trigonometry, the cosine rule is used, because it involves the adjacent and the hypotenuse.
Cos 51°=x/58
Let the size of the leg be x
Making x the subject
x=58(Cos51°)
x=36.500058
Correct to two decimal place
x=36.50
There are 10,000 people at a concert.
Of those people, 6,250 are adults.
What percent of the people at the
concert are adults?
Answer:
62.5%
Step-by-step explanation:
Total number of people at the concert = 10000
Number of adults = 6250
Percentage of adults = number of adults/ total number of people at the concert x 100%
That’s
6250/10000 x 100%
0.625 x 100%
62.5%
62.5% of the people at the concert are adults
What is the value of x?
The value of x is 8√2.
Step-by-step explanation:
From the right triangle,
The angles are 90°, 45° and the third angle is unknown.Third angle = 180° - (90°+45°) = 45°The measure of third angle is 45°The length of the side opposite to angle 45° is a=8.
Therefore, the value of y opposite to angle 45° is also 8.(b=8)
Using Pythagorean theorem,
The length of hypotenuse is c ⇒ c² = a²+b²
c² = 8²+8²
c² = 64+64 = 128
c = √128
c = √64[tex]\times[/tex]2
c = 8√2
So every week in my class we do a riddle and if you’re able to solve 3 of these correctly in a row you get a prize (homework pass, money or candy etc) and this would be my 3rd one correct in a row but I want to make sure my answer is right. Please help!
Answer:
18 but look at others awnsers aswell
Step-by-step explanation:
Answer:
Their is a total of 12 rectangles in the picture
Step-by-step explanation:
All of the figures located in the picture are all rectangles
How many liters are in 8 quarts?
Answer:
7.57082 liters
Step-by-step explanation:
2. what value of b makes the following equation true
3. which statement is true about the value of
Answer:
2. 10
3. D. 1 for all n
Step-by-step explanation:
2. The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^b = 1/a^-b
__
[tex]\dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}[/tex]
The value of n is 10.
__
3. Using the above rules of exponents, the expression simplifies to ...
6^(-n+n) = 6^0 = 1
The value is 1 for any n.
Find the volume of a cone that has a radius of 5 centimeters and a height of 7 centimeters.
Volume = cm³
(Use 3.14 for pi and round your answer to the nearest hundredth.)
Volume of the cone is 200 cm³
Step-by-step explanation:
Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 5 inches and h = 7 inches.Volume = 1/3 × 3.14 × 5² × 7
= 183.17 in³ ≈ 200 cm³ (rounding off to nearest hundredth)
please help me with this problem
Answer: The answer would be the third option 4/4 x 6 = 6
Answer:
4/4 x 6 = 6
Step-by-step explanation:
This is the answer because 4/4 is one which means 1 x 6 = 6 so they are the same.
the area of a circle is 36/pi cm^2 What is the radius of the circle?
Answer:
the radius of the circle is 6cm
Step-by-step explanation:
the area of a circle is given to be = 36πcm²
radius of the circle = ?
to find the radius of the circle lets start by applying the formula for finding the area of a circle.
area of a circle = πr²
36πcm² = πr²
36π = πr²
divide both sides by π
36π/π = πr²/π
36 = r²
to get the value of r we are going to look for a way of getting rid of the square on "r" by squaring 36
r² = 36
r =√36
r = 6cm
therefore the radius of the circle is 6cm
Answer:
6 cm
Step-by-step explanation: