Answer:
$3.00
Step-by-step explanation:
Jose receives $1270 per year from three
different investments totaling $20,000. One of
the investments pays 6%, the second one pays
8%, and the third one pays 5%. If the money
invested at 8% is $1500 less than the amount
invested at 5%, how much money has Jose
invested in the investment that pays 6%? SET
UP BUT DO NOT SOLVE.
The answer is. $1500.
Let x represent the amount invested at 5%, then is the amount invested at 8%, and is the amount invested at 6%. Since the total return is $1270:
let money invested at 5%= x
money invested at 6%
= 20000- (X+X-1500)
21500-2x
Total interest for 1 year.
x×5/100+ (x-1500)×8/100+(21500-2x)×6/100 = 1270
5x/100+8(x-1500)/100+(21500-2x)6/100=1270
5x+8x-12000+129000-12x = 127000
x+117000 = 127000
x = 10000
money invested at 8%
=21500-2×10000
= 1500.
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Solve each equation. Check your answers. 2 ln x+3 ln 4=4
On solving the logarithmic function, 2 ln x+3 ln 4=4, we get value of x as is x = √e⁴ - 63.
What is the logarithm function ?In mathematics, the opposite of exponentiation is the logarithm. This means that the logarithm of a given number, base b, represents the exponent to which that number must be increased in order to get a certain number, x.
Given equation is -
2 ln x + 3 ln 4=4
⇒ ln x² + ln 4³ = 4
⇒ ln (x² + 4³) = 4
⇒ taking e
⇒ log e(x² + 4³) = 4
⇒ e⁴ = x² + 4³
⇒ e⁴ = x² + 63
⇒ x = √e⁴ - 63
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True or false. any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by two and five?
You collect $234 selling small and large smoothies. you sell a total of 46 smoothies. how many of
size did you sell?
The number of small smoothies sold is 26.
The number of large smoothies sold is 20.
What is the number of each size sold?The first step is to form a pair of simultaneous equations:
s + l = 46 equation 1
4s + 6.5l = 234 equation 2
Where:
s = number of small smoothies sold
l = e number of large smoothies sold
Multiply equation 1 by 4
4s + 4l = 184 equation 3
Subtract equation 3 from equation 2
2.5l = 50
Divide both sides of the equation by 2.5
l - 50 / 2.5
l = 20
Subtract 20 from 46
s = 46 - 20 = 26
Here is the complete question:
You collect $234 selling small and large smoothies. You sell a total of 46 smoothies. A small size is $4 and a large size is $6.50. How many of each size did you sell?
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Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 2%?.
If scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score you would need to be in the top 2% is equal to 88.929.
This type of problem can be referred to as a normal distribution problem.
It can be solved by using the z-score.
Formula;
Z = x - μ / σ
Here,
Z represents the standard score
x represents the observed value
μ represents the mean
σ represents the standard deviation
The z- score can be found by using the p-value on a standard table.
As the minimum score to be in the top 2% is needed to be found, p-value = 0.02
z- score that corresponds to the p-value of 0.02 in the standard table is equal to 2.054
Hence,
2.054 = x - 76.4 / 6.1
2.054(6.1) = x - 76.4
12.529 = x - 76.4
x = 12.529 + 76.4
x = 88.929
Hence the minimum score needed to be in the top 2% is calculated to be 88.929
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eighty students are going on a field trip to a history museum. The total cost includes 2 bus rentals and $10 per student for lunch. Write and evaluate a numerical expression to find the total cost per student for the field trip.
Use natural logarithms to solve each equation.
ex/₅+4=7
-10.27 is the value of x in equation [tex]e^{\frac{x}{5} + 4}[/tex] = 7 solved by using natural logarithms
We have been asked to find x in [tex]e^{\frac{x}{5} + 4}[/tex] = 7 using natural logarithms
⇒ [tex]e^{\frac{x}{5} + 4}[/tex] = 7
⇒ [tex]\frac{x}{5}[/tex] + 4 = ㏑(7)
⇒ [tex]\frac{x}{5}[/tex] = ㏑(7) - 4
⇒ x = ㏑(16807) - 20
= -10.27
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^{\frac{x}{5} + 4}[/tex] = 7
Select the values that make the inequality -a<4 true.
Then write an equivalent inequality, in terms of aa.
(Numbers written in order from least to greatest going across.)
The values that satisfy the inequality are -3 , 0 , 14 .
A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. On the number line, size comparisons between two numbers are typically conducted. Different notations can be used to represent various kinds of inequalities, including:
The symbol a <b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.
Now the given inequality is of the form -a < 4
solving we get:
a > - 4
Therefore the number which will satisfy this inequality are:
-3 , 0 , 14 .
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Find the slope-intercept form of the equation of the line that passes through the points
(2, -1) and (-3, 4)
Answer:
-1
Step-by-step explanation:
Use slope formula.
y2-y1/x2-x1
(2, -1) and (-3, 4)
4+1/-3-2=
=5/-5=-1
The slope is -1. The line is slanted down from left to right.
Hope this helps!
Please mark as brainliest if correct!
Answer:
y = - x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 1 ) and (x₂, y₂ ) = (- 3, 4 )
m = [tex]\frac{4-(-1)}{-3-2}[/tex] = [tex]\frac{4+1}{-5}[/tex] = [tex]\frac{5}{-5}[/tex] = - 1 , then
y = - x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 3, 4 )
4 = 3 + c ⇒ c = 4 - 3 = 1
y = - x + 1 ← equation of line
6. The table shows the volume of water in
cubic meters, V, in a tank after water has
been pumped out for a certain number of
minutes.
Which equation could represent the
volume of water in cubic meters after t
minutes of water being pumped out?
A. V = 30-2.5t
B. V = 30-0.5t
C. V = 30-0.51²
D. V = 30-0.11²
The correct option is D. V = 30-0.1t² ; represents the the volume of water in m³ after t minutes of pumping.
What is defined as the volume of water?Volume is a measurement of how much space an object occupies. Whenever a cylinder is immersed in water, it pushes water away. The volume of water pushed out of way can be calculated by measuring the amount this same water level rises.For the given question;
The values for the time of pumping and the volume of water is given;
use them to find the equation which represents their relation.
when, time t = 5
put the values in the options.
a. V = 30 - 2.5 × 5 = 17.5 .....(wrong)
b. V=30 - 0.5 × 5 = 27.5 .....(correct)
c. V = 30 - 0.5 × 25 = 17.5 ......(wrong)
d. V = 30 - 0.1 × 25 = 27.5 ........(correct)
Now, check at time t = 10 just for the correct value.
b. V = 30 - 0.5 × 10 = 25 .....incorrect
d. V = 30 - 0.1 × 100 = 20 ......correct
Therefore, the relation of the water pumped with time is given by the relation; V = 30-0.1t².
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The complete question is-
The table shows the volume of water in cubic meters, V, in a tank after water has been pumped out for a certain number of minutes.
Which equation could represent the volume of water in cubic meters after t minutes of water being pumped out?
A. V = 30-2.5t
B. V = 30-0.5t
C. V = 30-0.5t²
D. V = 30-0.1t²
(f) Belinda buys a flat screen plasma television costing R20 000 on hire purchase. She traded in an old television for R3 000 and paid a deposit of R 2000. The balance was paid by means of monthly instalments of R900 over two years. Calculate the total simple interest paid and the rate of simple interest.
The total simple interest paid by her is R6,600 and the rate of simple interest is 22%.
Given that
Belinda buys a flat screen plasma television costing R20 000 on hire purchase.She traded in an old television for R3 000 and paid a deposit of R 2000.The balance was paid by means of monthly instalments of R900 over two years.To find
Simple interest paid and Rate of simple interest.So, according to the question
We have,
Cost of television = R20,000 Selling price of old television = R3,000Deposit by her = R 2,000.After trading in and depositing, the balance was as follows:
= Cost of television - Selling price of old television - Deposit by her
= 20,000 - 3,000 - 2,000
= R15,000
The total simple interest paid by her in 2 years:
= (900 x 2 x 12months) - 15,000
= R6,600
The rate of simple interest given by her in 2 years:
= (6,600 / 2 years) / 15,000
= 22%
The total simple interest paid by her is R6,600 and the rate of simple interest is 22%.
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Write each expression as a single natural logarithm. ln 24- ln 6
Expression as a single natural logarithm is 1.38629436112
What is natural logarithm?ln 24- ln 6
ln(24/6)
ln 4 = 1.38629436112
The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.
The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).
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ASAP PLEASE HELP IF RIGHT ANSWER WILL GIVE BRAINLIEST, 15 POINTS, AND 5 STAR OVERALL!!!! IF WRONG ANSWER OR INVALID WILL REPORT, PLEASE, PLEASE, PLEASE!!
Answer:
Slope or (m) = 1 Give Brain
Multiply.
(−56)⋅58
What is the product?
Enter your answer, as a fraction, in the box.
Answer:
the answer for this question is -3,248
Find the inverse of each function. Is the inverse a function? f(x)=∛x/3
The inverse for the function f (x) = ∛x / 3 will be f ⁻¹ (x) = 3 x³.
We are given the function:
f (x) = ∛x / 3
we need to find the inverse of the function.
First we will write the function in the form of x.
y = ∛x / 3
y³ = x / 3
3 y³ = x
x = 3 y³
So, the inverse function will be:
f ⁻¹ (x) = 3 x³
Therefore, the inverse for the function f (x) = ∛x / 3 will be f ⁻¹ (x) = 3 x³.
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ROSIE IS MY FAVORITE DOG
Answer:
A. Shawn's Poster
Step-by-step explanation:
It uses perimeter, and the formula is L*W.
Christie hiked 1/4 and Jackie hiked 3/5 MORE. More means Subtraction so it would be [tex]\frac{3}{5} -\frac{1}{4}[/tex]
Same thing for the other two. They represent subtraction because of their keywords. Here is a list below of what you need to look for, for each control (+,-,x,÷)
Hope this helps
~R3VO
Damian has 2 rolls of ribbon. He has 63 m of pink ribbon and 105 m of green ribbon. He wants to cut all of the ribbon into smaller pieces of equal length, with no ribbon left over. Work out the greatest possible length that Damian could make the smaller pieces of ribbon. Give your answer in metres (m).
Damian should cut the ribbons into pieces of 21 meters.
What is the largest length in which Damian could cut the ribbon?
To answer this, we need to find the maximum common factor between the two lengths of ribbon, which are 63 and 105.
If we rewrite both of these numbers as a product between prime factors we get.
63 = 3*3*7
105 = 3*5*7
Then the maximum common factor between these two numbers is 3*7 = 21
Then we conclude that Damian should cut the ribbons into pieces of 21 meters.
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-4|6b-8|<12 pls help so confused
Answer:
b > 5/6 or b < 11/6
Step-by-step explanation:
1. Divide both sides by -4
[tex]\dfrac{-4(|6b-8|)}{-4} < \dfrac{12}{-4}[/tex]
2. Simplify above
[tex]|6b-8| > -3[/tex]
3. The absolute value of an expression means that the expression can be positive or negative
Here | | represents the absolute value of 6b-8
For an absolute value to satisfy the above inequality
either 6b - 8 > -3 or 6b - 8 < - (-3)
(This follows from the fact that if |x| > -a, x > -a
or x < -(-a) ) which is the same as x < a
First case: 6b - 8 > -3:
6b - 8 + 8 > -3 + 8 ( Add 8 to both sides)
==> 6b > 5
==> 6b/6 > 5/6 (Divide both sides by 6)
==> b > 5/6
Second case: 6b - 8 < 3
6b −8 + 8 <3 + 8 (Add 8 to both sides)
==> 6b<11
==> 6b/6 < 11/6 (Divide both sides by 6)
==> b < 11/6
Kari has a mass of thirty-eight and
ninety-seven hundredths kilograms.
What is her mass in standard form?
Answer:
38.97 kilograms
Step-by-step explanation:
38 ones and 97 hundredths
38 0.97
38.97
How many different possible outcomes are there if you spin 3 spinners labeled Red, Blue, Yellow?
The number of possible outcomes are 6 if we have 3 spinners labeled Red, Blue, Yellow by using permutations.
There are 3 spinners:
Red
Blue
and yellow.
Number of possible outcomes will be calculated by using permutation.
So, we get that:
Number of possible outcomes = 3 × 2
Number of possible outcomes = 6 ways.
Therefore, the number of possible outcomes are 6 if we have 3 spinners labeled Red, Blue, Yellow by using permutations.
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A box of breakfast cereal contains 432 grams and 16 servings. How many grams are in one serving?
one serving is 432/19=27
27g are in one serving
Can someone please help me with this??
The equation of the circle with center at (-1, 5) and passes through the point (2, 9) is equal to (x + 1)² + (y - 5)² = 25.
The equation of a circle.Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r represents the radius of a circle.Next, we would determine the length of the radius (r) by using the distance formula. Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substituting the given parameters into the formula, we have;
Radius = √[(2 - (-1))² + (9 - 5)²]
Radius = √[(2 + 1)² + (4)²]
Radius = √[3² + 4²]
Radius = √[9 + 16]
Radius = √25
Radius = 5 units.
For the equation of a circle, we have:
(x - h)² + (y - k)² = r²
(x - (-1))² + (y - 5)² = 25
(x + 1)² + (y - 5)² = 25
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Complete Question:
Write the equation of the circle with center at (-1, 5) and passes through the point (2, 9).
You put 7 tiles with the letters A through G into a bag. You reach in without looking and
pull out 3 tiles and place them in a row. What is the probability that they spell BAG?
Express your answer as a decimal rounded to the nearest thousandth.
Having 7 tiles named A to G in a bag and picking 3 of them have the probability that they'll spell BAG is 0.0050.
What is probability ?Probability is the chance of occurring a certain event out of the total possible events that can occur in a given scenario.
According to the given question you put 7 tiles with the letters A through G into a bag.
Total no. of sample space N(S) = 7.
∴ The probability of getting getting B named tile P(B) is = 1/7.
Now as we are not replacing the tiles there are 6 tiles now so probability of getting A named tile P(A) = 1/6 and in the same way probability of getting G named tile is P(G) = 1/5.
∴ The probability that they will spell BAG P(BAG) is = (1/7)×(1/6)×(1/5) = 0.0050.
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Evaluate each expression for x=-2,0 , and 2 .
-(3)⁰.⁵x}
The result of the expression -(3)⁰.⁵x for x = -2 is 3.4, for x = 0 is 0 and for x = 2 is - 3.4
The question states to evaluate the given expression, that is, -(3) ⁰.⁵ x for the given values of x, that are, x = -2, x = 0, and x = 2.
This question can be easily solved by using the concept of substitution. We have to substitute the given values of x in the given expression one after the other and note the answer.
For x = -2.
we get, -(3) ⁰.⁵ ( - 2) = - 1.7 * (-2) = 3.4
For x = 0.
we get, -(3) ⁰.⁵ ( 0 ) = - 1.7 * ( 0 ) = 0
For x = 2.
we get, -(3) ⁰.⁵ ( 2 ) = - 1.7 * ( 2 ) = - 3.4
Therefore, we get the result of the expression -(3)⁰.⁵ x for x = -2 as 3.4, for x = 0 as 0 and for x = 2 as - 3.4
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Please help! Ty very much!
What is the value of test_val after the following code is executed? a = 12 test_val = 6 if a * 2 == test_val: a = a 7 else: test_val = 2 * a test_val = a 1
The value of test_val after the following code is executed is: 13.
What is Python?Python can be defined as a high-level programming language that is designed and developed to build websites and software applications, especially through the use of dynamic commands (codes or semantics) and data structures.
What is a variable?A variable can be defined as a specific name which refers to a location in computer memory and it is typically used for storing a value such as an integer or string.
Based on the given Python code, we have:
if a * 2 == test_val:
if 12 * 2 ≠ 6:
Therefore, we have:
test_ val = a + 1
test_ val = 12 + 1
test_ val = 13.
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1. Your friend sends you to the store with $20.
a) She needs bread, 3 cans of beans, and something dairy. How much do each cost? How much will
that cost in total?
b) Your friend says you can get a snack if you have enough money left over. Can you get a snack? How
much did you spend shopping? Include the amount
c) What snack did you buy
Which expression represents another method of computing the product given below?
-1.45*76
A.
(-1)((1 × 76) + (0.45 × 76))
B.
(-1)(-1.45 - 76)
C.
(-1)(-1.45 + 76)
D.
(-1)(-1.45 × 76)
The value expression represents another method of computing the product given
Thus option A. (-1)((1 × 76) + (0.45 × 76)) has value -110.2 . So it is correct option.
-1.45*76 =-110.2
Now checking all the option one by one if any option has the value -110.2
then it is correct
A. (-1)((1 × 76) + (0.45 × 76))
(-1)(76 + 34.2)
=-110.2
B. (-1)(-1.45 - 76)
(-1)(-77.5)
= 77.5
C. (-1)(-1.45 + 76)
(-1)(74.5)
= -74.5
D. (-1)(-1.45 × 76)
(-1)(-110.2)
= 110.2
Thus option A. (-1)((1 × 76) + (0.45 × 76)) has value -110.2 . So it is correct option.
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Let u= (-1,3), v=(2 , 4) , and w=(2,-5) . Find the component forms of the following vectors. (3/2)v
Given u = (-1, 3), v = ( 2, 4) , and w = (2, -5), by applying scalar multiplication of vectors, ³/₂ v = (3, 6)
In the 2D coordinate system, vectors can be split into x-component and y-component.
We can write, for example, a vector s = (4,–1), which means:
x-component = 4
y-component = –1
Some vector operations:
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1, 3), v = ( 2, 4) , and w = (2, -5)
Then,
³/₂ v = ³/₂ . (2, 4)
= ( ³/₂ . 2, ³/₂ . 4)
=(3, 6)
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8 ײ + 3× -10
- 2ײ +8 × + 10
please solve and give a solution thankyou
Answer:
6x²+11x
Step-by-step explanation:
1. Group like terms
[tex]8x^2-2x^2+3x+8x-10+10[/tex]
2. Add like terms
[tex]6x^2+3x+8x-10+10[/tex]
3. Add the numbers
[tex]6x^2+11x[/tex]