An amount of $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, one part of $2600 was invested at a rate of 7.5% and the other part was invested at a rate of 5%, and the total yield was $175 simple interest.
Let $x was invested at 7.5%, then $(2600-x) was invested at 5%.
Since the yield is $175, it follows,
7.5% of x + 5% of (2600-x) = 175
7.5x/100 + 5(2600-x)/100 = 175
7.5x + 13000 - 5x = 17500
2.5x = 17500-13000
2.5x = 4500
x = 1800
Now, the value of (2600-x) is,
2600-1800
=800
Hence, $1800 was invested at a rate of 7.5% and $800 was invested at a rate of 5%.
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William invested $1800 at 7.5% and $800 at 5% on his both accounts.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, William opened two investment accounts. In the first year, these investments, which totaled $2600,
Assuming he invested $x at 7.5% on the first account and $(2600 - x) at 5% in the second account and yielded $175 in simple interest.
∴ (x×7.5×1)/100 + {(2600 - x)×5×1}/100 = 175.
7.5x/100 + (13000 - 5x)/100 = 175.
7.5x + 13000 - 5x = 17500.
2.5x = 4500.
x = 1800. And (2600 - x) = (2600 - 1800) = 800.
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Solve the system of equations by graphing.
x+y=3
5x+5y=15
The system of equations are graphed in the image below, showing that they have infinitely many solutions, which include (3, 0) and (0, 3).
What is the Solution to the System of Equations?The values of a pair of x and y that will make two different equations in a system true is the solution to the system of equations.
By graphing, we can determine the solution by finding the x and y coordinates of the point that both lines of the equations intersect at.
The lines of x + y = 3 and 5x + 5y = 15 are graphed in the image below, which is the same blue line. This shows that the equations have infinitely many solutions such as (3, 0) and (0, 3).
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what is the best description of the first term in the expression below?
[tex](4x + 9) + \frac{x - 10}{6} [/tex]
A. sum
B. factor
C. product
D. quotient
Answer:
C
Step-by-step explanation:
The first term is 4x. The first term is the product of 4 and x.
determine if each ordered pair is a solution to the given system of linear inequalities in two variables.
Answer:
A. yes, B. yes,C. yes
Step-by-step explanation:
A. (3,0) yes
b. (4,-2) yes
c. (5,-4)yes
Assuming the assumptions of Analysis of Variance are satisfied, a higher F value means... (select all that apply)
a.
...a greater chance of rejecting the null hypothesis.
b.
...higher between-group variability relative to within-group variability.
c.
...a higher p value.
The higher F value means higher between-group variability relative to within-group variability. Option(b) is correct.
Analysis of variance (ANOVA) is a statistical formula used to compare variances between means (or averages) of different groups. It is used in a variety of scenarios to determine whether there is any difference in the means of different groups.
The F-value is the ratio of between-group and within-group variation. A high F-value indicates that the between-group variation is greater than the within-group variation. This can be interpreted as a statistically significant difference in the means of your groups.
A large f value (one greater than the F critical value found in a table) indicates that something is significant, whereas a small p-value indicates that all of your results are significant.
Therefore a higher F value the higher between-group variability relative to within-group variability.
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You can afford to spend at most 155 dollars per month on a cell phone plan. If your cell phone plan costs
20 dollars per month, plus 3 dollars per hour of call time how many hours can you afford to call?
A snack machine sells Crisps (C), Cereal Bars (B) and Soft Drinks (S). Jesse buys 2 different snacks at random.
List all the possible combinations of snacks she could buy. A possible combination would be Crisps and Cereal Bars, written as CB.
Note: Please separate your answers with a comma.
The possible combinations are
Crisps and Cereal BarsCereal Bars and Soft DrinksCrisps and Soft DrinksWhat is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
A snack machine sells Crisps (C), Cereal Bars (B) and Soft Drinks (S).
Jesse buys 2 different drinks at random.
So, the possible combinations for the drinks she buys are:-
CB, CS, BC, BS, SC, SB
Since the order in which Jesse bought the drink does not matter, the possible combinations are
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Find the number that is oppisit of 1/15 and 1/16
Answer:
The number opposite the product of 1/15 and 1/16 will be 240.
Step-by-step explanation:
Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The number opposite the product of 1/15 and 1/16 will be given as,
1
_____________
(1/15)*(1/16)
1
____
1/240
240
A certain element decays at a constant rate of 4% per year. If you start with 18 grams of the element, how long will it take before there are only two grams left? Round your answer to the nearest whole number.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & 2\\ P=\textit{initial amount}\dotfill &18\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years \end{cases}[/tex]
[tex]2=18(1 - 0.04)^{t}\implies \cfrac{2}{18}=(1 - 0.04)^{t}\implies \cfrac{1}{9}=0.96^t \\\\\\ \log\left(\cfrac{1}{9} \right)=\log(0.96^t)\implies \log\left(\cfrac{1}{9} \right)=t\log(0.96) \\\\\\ \cfrac{\log\left(\frac{1}{9} \right)}{ ~~ \log(0.96) ~~ }=t\implies 53.82\approx t\qquad \textit{about 53 years and 301 days}[/tex]
It will take approximately 54 years for the element to decay from 18 grams to 2 grams at a rate of 4% per year.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
To determine how long it takes for an element to decay from 18 grams to 2 grams, you can use the formula:
t = (ln(A/B)) / (-r)
where:
t is the time it takes for the decay to occur
A is the initial amount of the element, in this case 18 grams
B is the final amount of the element, in this case 2 grams
r is the decay rate, in this case 4% per year
Plugging these values into the formula gives you:
t = (ln(18/2)) / (-0.04)
t = (ln(9)) / (-0.04)
t = (2.1972) / (-0.04)
t = -54.30
Hence, It will take approximately 54 years.
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How to find each polynomial expression of 3x^2+2x+8
Using the factorization of polynomial, the factor of the given expression is (3x-4)(x+2).
In the given question we have to find the each polynomial expression of 3x^2+2x-8.
The given expression is 3x^2+2x-8.
Now finding the factor of the given expression.
The multiply of the first and third variable is 24. The middle term is 2.
So the possible factor is 6 and 4.
3x^2+2x-8 = 3x^2+(6-4)x-8
3x^2+2x-8 = 3x^2+6x-4x-8
3x^2+2x-8 = 3x(x+2)-4(x+2)
3x^2+2x-8 = (3x-4)(x+2)
Hence, the factor of the given expression is (3x-4)(x+2).
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The right expression is 3x^2+2x-8.
Suppose that white wool (W) is dominant over brown wool (w) in sheep. If two heterozygous sheep are crossed, what is the probability that their babies would have brown wool?
A:50%
B:75%
C:100%
D:25%
The probability that their babies would have brown wool will be 25%.
What is heterozygous?When two or more alleles for the same characters are present at the same loci on homologous chromosomes, a cell, a nucleus, or a single organism is said to be heterozygous. In contrast to homozygous, where the alleles are identical, it signifies that the alleles that code for the same gene or characteristic are different.
Given, the two-parent sheep would need to have heterozygosity for their genotype if we were to assume straightforward Mendelian genetics. Black would not be dominant in this situation; instead, the parents would be, shall we say, Rr for color. Imagine that each parent can only contribute one allele (either the R or the r). If both should chance to deliver the r, the child would be black.
Therefore, 25% of the following generation's children are likely to be black. There would be a 25% probability of a homozygous dominant offspring, a 50% chance of a heterozygous offspring, and a 25% chance of a homozygous recessive offspring if you filled out a Punnett square for this issue. Since white is the dominant allele in this situation, both the homozygous dominant allele, which accounts for 75% of the possibilities and the heterozygous child will be white. Since two recessive alleles are required to manifest the recessive phenotype, the remaining 25% of people are black.
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A cellphone provider has the business objective of wanting to determine the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results indicate that 110 of the subscribers would upgrade to a new cellphone at a reduced cost. Reducing the price will be profitable if at least 20% of the subscribers would upgrade. Complete parts (a) and (b) below
b. What is the test statistic?
The test statistic, using the z-distribution, is given as follows:
z = 1.12.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the proportion is greater than 20%, that is:
[tex]H_0: p \leq 0.2[/tex]
At the alternative hypothesis, it is tested if there is evidence that the proportion is greater than 20%, that is:
[tex]H_0: p > 0.2[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables of the equation are listed as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]p = 0.2, n = 500, \overline{p} = \frac{110}{500} = 0.22[/tex]
Hence the test statistic is given as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.22 - 0.2}{\sqrt{\frac{0.2(0.8)}{500}}}[/tex]
z = 1.12.
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What's the slope of a line that passes through the points (1,−2) and (2,2)?
The slope of a line that passes through the points (1,−2) and (2,2) is 4.
The two given points are (1,-2) and (2,2).
We have to find out the slope of the line that passes through the two given points.
We know that the slope of a line passing through two points ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) is -
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Using this formula for the given points (1,-2) and (2,2), we can find out the slope of the line passing through them as -
[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\= > m = \frac{2-(-2)}{2-1}\\ = > m = \frac{4}{1}\\ = > m = 4[/tex]
Thus, the slope of a line that passes through the points (1,−2) and (2,2) is 4.
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36.8 divided by [11.5- (6.25)]
Answer:
7.00
Step-by-step explanation:
36.8/ (11.5-6.25) = 7.00952380952 Now just pick two first numbers two there you go. Dam being a 6 grader Wow
Let g(x)=x-5.
Find x when g(x) = -5.
Answer:
x = 0
Step-by-step explanation:
Substitute g(x) for x-5 in the equation,
x-5 = -5
collect like terms or add 5 to both sides
x = -5+5
x = 0
Find -12x for each value of x.
Value of x value of -12x
2
4
-3
6
A paper company need to ship paper to a large printing house. The paper will be shipped in small boxes and large boxes. The volume of each large box is 14 cubic feet. A total of 21 boxes of paper were shipped with a combined volume of 252 cubic feet. Write a system of equation that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you can use to white the system.
Answer:
See belowStep-by-step explanation:
Let the number of small boxes is s and number of large boxes is l.
s and l are our variables.
Total number of boxes is 21:
s + l = 21This is your first equation.
The volume of a small box is a (since it is not given, if you have it please replace it with that number), and the volume of all small boxes is as.
The volume of a larger box is 14 cubic feet, and the volume of all large boxes is 14l cubic feet.
Total volume is 252 cubic feet, add the two volumes together:
as + 14l = 252And this is your second equation (don't forget to replace a with the volume of a small box).
Find the square root of
441
Answer:
21
Step-by-step explanation:
√441
Take factors of 441
-> 1,3,7,9,21,49,63,147,441
If you know all of them like this and it’s an odd number, find the middle value that doesn’t have a pair and it’s 21.
If you don’t just take a different value that has a square root. Let’s do 9.
Separate the root into √9*49
Woah, both of those are squares!!
Take the square root of both of those numbers
√9*√49
3*7=21, voila.
It is very easy, we just have to take the square root as it tells us in the problem:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{ \sqrt{441 }} = \orange{21}[/tex]
You may ask ¿why 21?
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{21 \times 21} = \orange{441} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf So , \: the \: result \: is \\ \sf \: \: \: \: \longmapsto \orange{21} [/tex]
Find the equation of a line that passes through the point (5,3) and has a gradient of 2. Leave your answer in the form y = m x + c
The equation of the line in slope intercept form is y = 2x - 7..
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line that passes through (5,3) and has a gradient of 2 can be found as follows;
m = 2
let's find the y-intercept using (5, 3)
3 = 2(5) + b
b = 3 - 10
b = -7
Therefore, the equation of the line is y = 2x - 7.
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2.3² + √5.6
Help me please
Answer:
7.65643191
Step-by-step explanation:
2.3^2 = 5.29 √5.6 = 2.36643191324
5.29 + 2.36643191324 = 7.65643191
Find the number that is opsite of 1/15 and 1/16
Answer:
The number opposite the product of 1/15 and 1/16 will be 240
Step-by-step explanation:
1
____________
(1/15) x (1/16)
1
____________
1/240
240
What is Algebra?
Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The number opposite the product of 1/15 and 1/16 will be given as,
Amy weighs 150 pounds on earth and 350 on another planet. Find West lose weight on that planet if he weighs 130 pounds on earth.
Answer:
do you speak English
Step-by-step explanation:
Amy weighs 150 pounds on earth and 350 on another planet. Find West lose weight on that planet if he weighs 130 pounds on earth.
Complete the number sentence.
2 + (-10) = ?
-9 + (-13) =?
-25 + ? = -9
? + (-13) = -29
Solve for m. 2 - 6m = -4m+10 (m=__) also 2.5+1.75= -3.25+1.5x (x=__)
Value of m is -4
Value of x is 5
To solve linear equations, follow the following steps:
Clear fractions and decimals.Simplify each side of the equation by removing parentheses and combining terms.Isolate the variable term on one side of the equation keeping the other terms separateSolve the equation by dividing each side of the equation mathematicallyMatch your steps and the final solution with the correct solutionEquation 1.
2-6m = -4m+10
6m-4m = 2-10
2m = -8
m = -8/2
m = -4
Value of x is -4
Equation 2.
2.5+1.75 = -3.25+1.5x
1.5x = 4.25+3.25
1.5x = 7.5
x = 7.5/1.5
x = 5
Value of x is 5
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What is 5×5 Please give me the answer show your work
Answer:
It is the method by multiplication
Step-by-step explanation:
5×5=25
Learn at brainlyWhat is the best search engine for Musical Instrument and Sound Effects in MP3 Audio Online?
The best search engine for Musical Instrument and Sound Effects in MP3 Audio Online is MP3 realm.
What is MP3?MP3 is a digital audio coding format developed primarily by the Fraunhofer Society in Germany, with assistance from other digital scientists in the United States and elsewhere.
MP3 (MPEG-1 Audio Layer-3) is a standard technology and format for compressing a sound sequence into a small file (about one-twelfth the size of the original file) while maintaining the original level of sound quality when played. MP3 files, which take up very little hard drive space, are commonly used to store a song or an entire CD.
MP3 Realm is a music search engine that allows you to find MP3 tracks from all over the Internet.
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Pleaseeee help me. I'm stuck on a math question.
The slope of the function for pronghorn antelope is 60.78 which infers that the rate of speed of the pronghorn is 60.78 miles per hour.
7) The given function that represents the speed of the pronghorn is
y = 60.78x - 5.4
Comparing this function with the general equation of a straight line
y = mx + c we can conclude that the slope of the function is 60.78 .
So the Pronghorn's rate of speed is 60.78 miles per hour.
8) Now the speed of the cheetah is given in the form of a table.
Let us take any two points on the graph
(0.5,21.85) and (2,118.60)
Slope of the line passing through these two points
= (118.6-21.85)/(2-0.5)
=64.5
So the slope of the graph is 64.5 and the average rate of speed of the Cheetah is 64.5 miles per hour.
9) From the above two slopes and the rate of speed we can conclude that the speed of the cheetah is 64.5 mph which is greater than that of the pronghorn 's speed of 60.78 miles per hour.
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You flip three coins eight times. Are you guaranteed to get three heads at least once
When one flip three coins eight times, there no guarantee to get three heads at least once as the probability is low.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
The probability of getting a head in a coin is 1/2.
Therefore, the probability of getting three heads on there flips will be:
= P(head)³
= 1/2 × 1/2 × 1/2
= 1/8
Therefore, the probability is low and the heads aren't guaranteed.
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2. Write the correct equation that you would use to solve for side x.
Z
X
520
y = 13cm
Z
Y
Answer: Using SOH CAH TOA you get 10.24
Step-by-step explanation:
you can determine what the value of X is and it is 10.24
This is gotten by sin52=x/13
Because we are trying to get x which is opposite the angle, and we have the value of the hypotenuse already (13) we can using SOH that is sin 52= x divided by 13
Cross multiply and you'll get 10.2441398
A city administrator with a $100,000 annual budget is trying to decide between fixing potholes or directing traffic at several busy intersections after school. Studies have shown that 15 cars hit potholes every week, causing average damages of $200. Collisions at the intersections are less frequent, averaging one per month at an average cost of $6,000, although none have ever caused injuries or deaths. Use this information to answer the following questions.
1. What are the annual costs from the pothole damage?
2. What are the annual costs due to damage from
collisions?
3. Given the size of the annual budget, make your
recommendation as to which project should be
undertaken. Explain you answer in terms of dollar
benefits per dollar spent.
1. The annual costs from the pothole damage is $156428.
2. The annual costs due to damage from
collisions is $72000 per year.
3. The project should be undertaken
How to calculate the value?1. The budget is given as $100,000
The number of cars hit potholes per week = 15
Number of cars hit potholes per year = 15*52.148
= 782.14 cars
Total amount of damage per year will be:
= 782.14 * 200 = $156428
2. Number of collusion at intersection per month = 1
Number of collusion at intersection per year = 1 * 12 = 12
Total cost of collusion at intersection per year = 12*6000
= $72000 per year
3. Saving on potholes = 156248 / 100000 = $ 1.56
Saving on collusion at intersection:
= 72000 / 100000
= $0.72
So from above, it is clear that if the budget is spent on potholes, more savings will be done. Thus the budget should be invested in potholes.
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A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.M. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 8.8 gallons. What is the average rate of flow of the gasoline into the gas tank?
The average rate of flow of gasoline into the gas tank is 2.2 gallons per minute.
What is the average?The average is the mean value of the data set values.
The mean is computed by dividing the total value by the number of items.
For the average rate of flow, divide the total gallons of gasoline filled by the driver, 8.8 gallons, by the number of minutes used in filling the tank.
In this case, the average rate of flow shows the speed that the driver used to fill the car with gasoline.
Starting time = 3:40 P.M.
Ending time = 3:44 P.M.
The difference in filling time = 4 minutes (3:44 - 3:40)
Total number of gallons of gasoline filled = 8.8 gallons
Average rate of flow of the gasoline = 2.2 gallons per minute (8.8/4)
Thus, at an average rate of 2.2 gallons per minute, the driver was able to fill his gas tank in 4 minutes.
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