$6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.
What is annual interest rate?
An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.
Invested amount = $7000
Let x be the invested amount at 6% and y be the invested amount at 8%.
According to the question,:
x+y=7000......(1)
annual interest is $430.
Therefore Interest on x + interest on y = $430
Interest=(invested amount*rate*time)/100
Here Time is 1 year.
(6*x)/100+(8*y)/100=430
This shows, 6x+8y=43000.......(2)
From equation (1), we have:
x=7000-y.........(3)
Substitute the value of x in equation (2),
6(7000-y)+8y=43000
On simplifying, y=500
Put y = 500 in equation (3)
we get x=6500
Therefore $6500 is invested at the rate of 6% and $500 is invested at the rate of 8%.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Match the picture with the correct vocabulary for the 2 angles shown.
Answer:
3: alternate exterior angles 4: supplementary angles
Step-by-step explanation:
3: they are outside, on dif sides.
4: same side, and make 180 degrees
The legs of a right triangle are 18 centimeters and 80 centimeters long. What is the length of the hypotenus: 82 or 85 or 89 or 98
Answer:
82
Step-by-step explanation:
1.) Recognize that this is the Pythagorean Triple 9, 40, 41, just multiplied by two (9*2 = 18, 40*2 = 80).
2.) Now, to find the third number, we just multiply 41 by 2 to get 82.
Answer:
The hypotenuse is equal to 82 centimeters.
Step-by-step explanation:
Using the Pythagorean theorem (a^2 + b^2 = c^2), which states that the legs of a right triangle (a and b) squared, equal the hypotenuse squared, we can plug in the values of the legs of the right triangle into spots a and b. This gets us the equation 80^2 + 18^2 = c^2. We can then square the values to get 6400 + 324 = c^2. We then get 6724 = c^2, and then take the square root of both sides to get the value of c, the hypotenuse. This gets us c = 82, so the hypotenuse is equal to 82 centimeters.
Babe Ruth, a professional baseball player known for hitting home runs, had a batting average of 0.342. Hank Aaron, another record home run hitter, had a batting average of 0.305.
3.7% greater was Babe Ruth's batting average than Hank Aaron's.
Given that, Babe Ruth, a professional baseball player known for hitting home runs, had a batting average of 0.342.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
According to the question, 0.342-0.305
= 0.037
Now, 0.037 × 100
= 3.7%
Hence, 3.7% greater was Babe Ruth's batting average than Hank Aaron's.
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"Your question is incomplete, probably the complete question/missing part is:"
Babe Ruth, a professional baseball player known for hitting home runs, had a batting average of 0.342. Hank Aaron, another record home run hitter, had a batting average of 0.305. How much greater was Babe Ruth's batting average than Hank Aaron's?
Using the graph below, determine the employee's hourly wage.
By using the graph, the employee's hourly wages is calculated as $10.6
Graph:
Basically, a graph is a collection of points, called vertices, and lines between those points, called edges.
Given,
Here we have the graph with straight line.
And we need to determine the employee's hourly wage.
While we looking into the graph we have identified that the x axis refers the number of hours the employ is working and the y axis refers the money earned by them.
In order to find the wages for one hour, we need to select one point from the graph.
Here we have take the point (5,53)
The first point refers the number of hours that is 5.
And the second one refers the wages for 5 hours that is 53.
So, the one hour wages is calculated as,
=> 53/5
=> 10.6
Therefore, the employee's hourly wage is $10.6.
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The function f(x)
o 95 miles; f(3) represents the total distance remaining after 3 hours.
represents the total distance traveled after 3 hours.
O 95 miles; f(3)
O 165 miles; f(3)
represents the total distance remaining after 3 hours.
O 165 miles; f(3)
represents the total distance traveled after 3 hours.
= 260 - 551
represents the distance, in miles, remaining on a trip z hours into the trip. What is the value of f(3), and what does it represent?
f(x) represents the distance, in miles, remaining on a trip z hours into the trip. The value of f(3) is 95 miles and it represents the total distance remaining after 3 hours.
Define function.A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given,
Function:
f(x) = 260 -55x
When f(3)
f(3) = 250 - 55(3)
f(3) = 250 - 165
f(x) = 95
95 miles; f(3) represents the total distance remaining after 3 hours.
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4) Employees
at The Shoe Shack get a
25% discount when they buy a pair
of shoes at the store.
Theo wants to buy a pair of shoes with a regular price of $48.
What is the discount on a pair of shoes with a regular price of $48?
Answer: 12
Step-by-step explanation: 25% is always 25/100 or 1/4. To get this you have to multiply 48 by 1/4 with is 48/4 = 12$.
Hoped This Helped!
PLEASE HELP ME I’ll GIVE 20 PTS!!! The pizza shop offers a 15 percent discount for veterans and senior citizens. If the price of a pizza is $12, how would you find the discounted price?
Answer:
10.2
Step-by-step explain:
Subtract 15 from 100, you should get 85. Then move the decimal 2 times to the left from 85, then 12 and .85 and that is you answer.
Answer:
10.20
Step-by-step explanation:
12-15%= $10.20
And that's it just subtract with the % sign and you'll get the same
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 8ft Find the area of the shaded region.
Use the value 3.14 for PI , and do not round your answer. Be sure to include the correct unit in your answer.
it wont let me paste the picture but please help
Answer: 6.88 cm sq.
1. Find the area of the rectangle
A=l *w
L=8cm
the width=the radius of the semicircle
Width=8/2=4
8*4=32
A=32cm sq
2. find area of the semicircle
area=pi times the radius squared divided by 2
r=4cm
A=(3.14)*4^2/2. The area =25.12 cm sq.
Area of the shaded region=32-25.12=6.88cm sq.
Waskahat wants to make a pair of earrings of different sized circles. The diameter of the first circle is 10 cm and that of the second is 6 cm. For his project, Waskahat determines that 35 beads will cover an area of 1 cm². How many beads in total will he need to make BOTH circles? Please answer with a whole number.
The number of beads needed to make both pair of earrings is 3090.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The diameter of first circle is 10 cm.
The diameter of second circle is 4 cm.
And, the area covered by 35 beads is 1 cm².
Now, the area of first and second circle is given by substituting the diameters in the expression for area πD²/4 as,
Area of the first circle = (π × 10²)/4
= 25π cm².
Area of the second circle = (π × 4²)/4
= 4π cm²
The total area is 25π + 4π = 29π cm².
Now, the number of beads can be determined using the unitary method as below,
Number of beads for 1 cm² area is 35.
So, the beads for 29π cm² area is 35 × 29π = 3090.
Hence, the number of beads required for both the circles is 3090.
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7) Keith had 100 dollars to spend on 7 books. After
buying them he had 16 dollars. How much did each book cost?
8) Sally spent half of her allowance going to the movies. She washed the family
car and earned nine dollars. What is her weekly allowance if she ended with
sixteen dollars ?
9) Oceanside Bike Rental Shop charges 15 dollars plus 6 dollars an
hour for renting a bike. Joan paid 57 dollars to rent a bike. How many
hours did she pay to have the bike checked out ?
10) On Monday, one hundred sixty-nine students went on a trip to the zoo. All four
buses were filled and nine students had to travel in cars. How many students were
in each bus?
Answer:
7)
so
100-16=84
then
84÷7=12
each book costs 12 dollars
if 1,2 and 3 are the eigen values of A=[2 0 1; 0 2 0; a 0 2], find the value of a?
The value of ''a'' will be 1
What is Matrix?
A set of numbers arranged in rows and columns so as to form a rectangular array, is called Matrix.
Given that;
1,2 and 3 are the eigen values of matrix A.
Now,
We know that;
The product of eigen values of a matrix is equal to the determinant of that matrix.
So, We find the determinant of matrix as;
[tex]A = \left[\begin{array}{ccc}2&0&1\\0&2&0\\a&0&2\end{array}\right][/tex]
Hence, We get;
| A | = 2 (4 - 0) - 0 (0 - 0) + 1 (0 - 2a)
| A | = 8 - 2a
And, The product of eigen values = 1 x 2 x 3 = 6
Hence, We get;
| A | = 8 - 2a
6 = 8 - 2a
2a = 8 - 6
2a = 2
a = 1
Thus, The value of ''a'' will be 1
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Assume the hypothesis is false. What is the
truth value of the conditional? Assume
the hypothesis is true. What would be
a counterexample?
The conditional statement has a true truth value if neither the hypothesis nor the conclusion is true.
A conditional statement is phrased as follows if we have the two propositions P and Q:
Q if P is true.
where P denotes the premise and Q denotes the result
The following are conditional statements' truth values:
The conditional statement is true if P and Q are true.
The conditional statement is false if P is false and Q is true.
The Conditional statement is false if P is true and Q is false.
The conditional statement is true if P and Q are both false.
Therefore, the conditional statement's truth value is true if both the hypothesis and the conclusion are false.
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math geometry help help
Answer: w = 20 and the other side would be 16
Step-by-step explanation: based on the shortest side, it looks like all of the sides would be multiplied by 4 getting the answer above. The degree of all of the angels should be the same as the smaller triangle as it’s just a sized up version.
Sorry if it’s wrong, I’ve never used this program before. Good luck!
How can I solve 2/1 divided by 3/11 using the giant one method
Giant one method: It is the method in which we multiply any fraction and we get an equivalent fraction.
For example:
1/2 x 1 (giant one) can also be written as:
=> 1/2 x 8/8
=> 8/16
It is also the method in which we divide any fraction and we get an equivalent fraction.
For example:
21/30 ÷ 1 (giant one) can also be written as:
=> 21/30 ÷ 3/3
=> 7/10
Solving the question:
2/1 ÷ 3/11
Solving this we get
=> 2 x 11/3 = 22/3
Multiplying giant one (1) through the giant one method.
=> 22/3 x 1 (giant one)
Multiplying both numerator and denominator by 3.
=> 22/3 x 3/3
=> 66/9
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Measure of ∡5
(Hint: What theorem lets you compare ∡3 and ∡5?)
Answer:
mAngle5 = 52° by
Alternate Interior angles
Step-by-step explanation:
When you have a pair of parallel lines and a transversal (the line that crosses them both)
this set up makes 8 angles....ALL the angles are either the same measure or they add up to 180°. Literally, if you know the measure of ONE angle, you can find the measure of all 8 angles. Its only two different numbers for all 8.
So, for your problem the two angles are in between the parallel lines (interior) and on different sides of the tranversal (alternate). By the Alternate Interior Angle Theorem they are congruent. One of them is 52° so the other one is also 52°
3. Solve for x: 2x+4=x-6.
a. x=-12
b. x = 10
C. X=-16
d. x=-10
Answer:
D. x = -10
Step-by-step explanation:
2x + 4 = x - 6
combine like terms
1x = -10
-10
Emilio Ramirez has a 35%-off coupon and is purchasing a
3-light chandelier that has a regular price of $115.00.
a. What is the markdown?
b. What is the sale price?
c. What is the sale price using the percent paid method?
a) The markdown is $40.25 with the 35%-off coupon.
b) The sales price after the markdown is $74.75.
c) The Sales price using the percent paid method is $74.75.
What is the markdown?The markdown is the difference between the regular retail price and the amount paid for the item.
The markdown is a reduction in the cost or price of an item.
The markdown is the opposite of the markup, which increases the cost.
Coupon off = 35%
Regular price = $115.00
a) Markdown = $40.25 ($115 x 35%)
b) Sale price = $74.75 ($115.00 - $40.25)
c) The Sales price using the percent paid method = $74.75 ($115 x 1 - 35%)
Thus, Emilio Ramirez with a 35%-off coupon (markdown) paid $74.75 for a 3-light chandelier regularly priced at $115.00.
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Evaluate and match each expression on the left to its value on the right, when x = 9 and y = 6.
12 - x
x + 3y
4y - 10
xy
3
27
18
14
The correct matches for the given values of x and y can be found by substituting the values in the equations which are 12-x = 3, x+3y= 27, 4y-10=14, xy=54
What is an equation?
Equation is an expression which have equality symbol in between
It means an expression in variable is equal to the constant.
We are given that x= 9 and y=6
We are asked to match the possible value
i) 12 -x
To solve this we substitute x= 9 in the equation
12-9
=3
ii) x+3y
To solve this we substitute x = 9 and y=6
9+3(6)
=9+18
=27
iii) 4y-10
To solve this we substitute y=6
=4(6)-10
=24-10
=14
iv) xy
To solve this we substitute x = 9 and y=6
= 9(6
=54
Hence the correct matches are 12-x = 3, x+3y= 27, 4y-10=14, xy=54
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Jaxson has a collection of 200 coins. How many coins represent 5% of his collection?
Answer: 13 coins
Step-by-step explanation:
100% --> 260
1% --> 2.6
5% --> 13
Answer:
10 coins
Step-by-step explanation:
Jaxson has a collection of 200 coins. How many coins represent 5% of his collection?
5% = 0.05
200 * 0.05 = 10 coins
The probability of selecting a patient who has an PPO plan is 0.46. The probability of selecting a patient who is between the ages of 30 and 55 is 0.43. The probability of selecting a patient who has an PPO plan and is between the ages of 30 and 55 is 0.27. What is the probability of selecting a patient who has an HMO plan or is
between the ages of 30 and 55?
The probability of selecting a patient who has and PPO plan or is between the ages of 30 and 55 is 0.62
Given,
probability of selecting a patient who has an PPO plan=P(A)=0.46
probability of selecting a patient who is between the ages of 30 and 55=P(B)=0.43
probability of selecting a patient who has an PPO plan and is between the ages of 30 and 55 =P(A∩B)=0.27
then, to find the probability of selecting a patient who has and PPO plan or is between the ages of 30 and 55 i.e. P(A∪B) use formula,
P(AUB)=P(A)+P(B)-(A∩B)
P(AUB)=0.46+0.43-0.27
P(AUB)=0.62
Thus,the probability of selecting a patient who has and PPO plan or is between the ages of 30 and 55 is 0.62
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The trail is 2448 miles long. It begins in city a and ends in city be man Fred has hiked three eights of the trail before how many miles has he hiked
The number of miles which Fred has hiked according to the task content is; 918 miles.
How many miles has Fred hiked?It follows from the task content that the given trail in discuss is 2448 miles long and the actual number of miles hiked by Fred is to be determined.
Given; Trail distance = 2448 miles.
However, Fred has hiked three eights of the trail before;
It therefore follows from proportion that;
If; 1 trail = 2448 miles;
Then; 3 / 8 trail = 3 / 8 × 2448 miles.
= 918 miles.
On this note, the number of miles hiked by Fred is; 918 miles.
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Adan is writing a comic book. His publisher has requested that he turned 50 pages draft by one day. If he's written 40 pages what percent does he still need to complete?
The length of a rectangle is four more than twice its width. If the perimeter of the rectangle is 56 cm, what is the width of the rectangle?
The rectangle has its width to be 8 cm
How to determine the width the rectangle?From the question, we have the following parameters that can be used in our computation:
The length of a rectangle is four more than twice its width
The perimeter of the rectangle is 56 cm.
The above parameters imply that
L = 2W + 4
P = 2(L + W)
Where L represents the Length and W represents the width
The perimeter is given as 56
So, we have
2(L + W) = 56
So, we have
L + W = 28
Substitute L = 2W + 4 in L + W = 28
2W + 4 + W = 28
Evaluate
3W = 24
Divide by 3
W = 8
This means that the width of the rectangle is 8 cm a
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1/5X+8=1/10X+9
What’s the answer to this question?
1/5x+8=1/10x+9.
We move all terms to the left:
1/5x+8-(1/10x+9.)=0
The domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x+9.)!=0
x∈R
We add all the numbers together, and all the variables
1/5x-(1/10x+9)+8=0
We get rid of parentheses
1/5x-1/10x-9+8=0
We calculate fractions
10x/50x^2+(-5x)/50x^2-9+8=0
We add all the numbers together, and all the variables
10x/50x^2+(-5x)/50x^2-1=0
We multiply all the terms by the denominator
10x+(-5x)-1*50x^2=0
Wy multiply elements
-50x^2+10x+(-5x)=0
We get rid of parentheses
-50x^2+10x-5x=0
We add all the numbers together, and all the variables
-50x^2+5x=0
a = -50; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-50)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use the following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=25−−√=5
x1=−b−Δ√2a=−(5)−52∗−50=−10−100=1/10
x2=−b+Δ√2a=−(5)+52∗−50=0−100=0
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help. 20 points. this is a proportion question.
what does x = ?
Answer:
x = 7
Step-by-step explanation:
[tex]\frac{3}{x}=\frac{x-4}{7}[/tex]
==> cross multiply
[tex]3*7=x*(x-4)[/tex]
==> simplify
21 = x² - 4x
==> subtract 21 from both sides
0 = x² - 4x - 21
==> factorize by finding two numbers that multiply to -21 and add up to equal -4
0 = (x - 7)(x + 4)
==> set each factor to 0 and solve for x
0 = (x - 7) 0 = (x + 4)
7 = x -4 = x
We can now plug in the values of x into the proportion to see which are true.
[tex]\frac{3}{x}=\frac{x-4}{7}[/tex] [tex]\frac{3}{x}=\frac{x-4}{7}[/tex]
x = 7 x = - 4
[tex]\frac{3}{7}=\frac{7-4}{7}[/tex] [tex]\frac{3}{-4}=\frac{-4-4}{7}[/tex]
==> subtract 4 from 7 ==> subtract -4 from -4
[tex]\frac{3}{7}=\frac{3}{7}[/tex] [tex]-\frac{3}{4}=-\frac{8}{7}[/tex]
The only true answer is x = 7
The area of square $ABCD$ is 100 square centimeters, and $AE = 2$ cm. What is the area of square $EFGH$, in square centimeters?
The area of square EFGH is 68 square centimeters
What is the area of a geometric figure?The area of a geometric shape or figure is the area enclosed in its boundary.
Please find attached a possible drawing of the information in the question
The area of square ABCD = 100 square centimeters
Length of segment AE = 2 cm
Therefore;'
The side length of the square ABCD, s = √(100) = 10
The length of segment AB = 10 cm
AB = AE + EB (segment addition postulate)
10 = 2 + EB (substitution property of equality)
EB = 10 - 2 = 8
EB = 8 cm
∠CFG ≅ ∠AHE (alternate interior angles)
ΔCFG ≅ ΔAHE (ASA congruency postulate)
Similarly; ΔEBF ≅ ΔHAE (ASA congruency postulate)
BF = AE (CPCTC) = 2
[tex]\overline{EF}=\sqrt{\overline{EB}^2 +\overline{BF}^2}[/tex](Pythagorean theorem)
Therefore;
EF = √(8² + 2²) = √(68)
EF = √(68)
Area of a square = (Length of one side)²
Therefore, area of square EFGH = [tex]\overline{EF}^2[/tex]
Which gives; Area of square EFGH = (√(68))² = 68
The area of square EFGH is 68 square meters
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A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag. Please explain!
Answer:
Step-by-step explanation:
is enough to think it will work with the new system but not the new one that is already working on the old one
Given the function h(x)=-x^2+x+4, determine the average rate of change of the function over the interval −1≤x≤4
The average rate of change of the function h(x) = - x² + x + 4 is equal to 22 / 5.
How to determine the average rate of change of a function
In this problem we find the definition of a function and its interval regarding an average rate of change. Graphically speaking, the average rate of change of the function over an interval is represented by the slope of a secant line that passes through two function points related to the interval limits.
The average rate of change is represented by the following formula:
m = [h(b) - h(a)] / (b - a), for a ≤ x ≤ b
If we know that h(x) = - x² + x + 4, a = - 1 and b = 4, then the average rate of change is:
m = [h(4) - h(- 1)] / [4 - (- 1)]
m = [h(4) - h(- 1)] / 5
m = (- 4² + 4 + 4 + (- 1)² - (- 1) - 4) / 5
m = (17 + 5) / 5
m = 22 / 5
The average rate of change is equal to 22 / 5.
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A rancher has 444 feet of fencing to enclose two adjacent rectangular corrals. The wall separating the two
corrals consists of a single fence. What dimensions for one of the individual corrals will produce the largest
total area?
Answer:
2 lengths and 3 widths
444 = 2*L + 3*w --> L = (444 - 3w)/2 = 222 - (3/2)w
Area = length x width
Area (w) == (222 - (3/2)w ) w
The max occurs at the average of the zeros.
The zeros are 222 - (3/2)w = 0 or w=0
222 = (3/2)w or w=0
w = 444/3=148 or w=0
The average is (444/3 +0)/2 = 222/3=74
width is 74 and length is 222 - (3/2)(74) = 222 - 111 = 111
The max area is 74 * 111 = 8214
To practice for a competition, Barry swam 730 meters in the pool each day for 4 weeks. How many kilometers did Barry swim in those 4 weeks? 1 m = 0.001 km
Answer:
20.44 km
Step-by-step explanation:
The values are,
→ 730 m = 0.730 km
→ 4 weeks = 28 days
Now Barry swam in 28 days is,
→ 0.730 × 28
→ 20.44 km
Hence, answer is 20.44 km.
