The first number is 3 and the second number is -5.
According to the question,
We have the following information:
There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.
Now, let's take the first number to be x and the second number to be y.
So, we have the following expressions:
6x+4y = - 2
6x = -2-4y ...(1)
6x+2y = 8
Putting the value of 6x from equation 1:
-2-4y+2y = 8
-2-2y = 8
-2y = 8+2
-2y = 10
y = -10/2
y = -5
Putting this value of y in equation 1:
6x = -2-4y
6x = -2-4*(-5)
6x = -2+20
6x = 18
x = 18/6
x = 3
Hence, the first number is 3 and the second number is -5.
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10. Reduce the fraction 36/48 to its lowest terms.
O A. 114
O B. %
O C. 112/48
O D.34
Answer:
if D is 3/4 then it is the answer
Step-by-step explanation:
Because both 36 and 48 can be divided by 12 and 36/12 = 3 and 48/12=4 so the answer is 3/4
Determine a so that A(t)=A0at describes the amount of nitrogen-16 left after t seconds, where A0 is the amount at time t=0. Round to six decimal places.
using the power rule of logarithm, the value of a is 1.1021.
In the given question we have to determine a so that [tex]A(t)=A_{0}a^t[/tex] describes the amount of nitrogen-16 left after t seconds, where [tex]A_{0}[/tex] is the amount at time t=0.
The given exponential function is [tex]A(t)=A_{0}a^t[/tex].
The amount of nitrogen-16 is approximately 7.13 seconds.
According to the question, [tex]A(t)=A_{0}/2[/tex] and t = 7.13 seconds.
Putting the value in the given function;
[tex]A_{0}/2=A_{0}a^{7.13}[/tex]
Divide by [tex]A_{0}[/tex] on both side, we get
[tex]1/2=a^{7.13}[/tex]
Taking In on both side
[tex]\text{In}(1/2)=\text{In}(a^{7.13})[/tex]
Using the power rule of logarithm
In(1/2)=7.13In(a)
Divide by 7.13 on both side
In(a)= -0.693/7.13
In(a)= -0.0972
Taking exponential on both side
[tex]e^{\text{In}(a)}= e^{-0.0972}[/tex]
a = 1.1021
Hence, the value of a is 1.1021.
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PLEASE HURRY I WANT TO FIISH MY TEST PLEASE ASAP!!!
Determine which integers in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false.
The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, based on the information we will replace m with 32. This will be illustrated thus:
1/4(32 - 4) ≤ 1/8 (32 - 16)
= 1/4(28) ≤ 1/8(16)
= 7 ≤ 2
In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.
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b) How many more squares need to be shaded so that 70% of the grid is shaded?
The percentage of shaded grid is 45% and the number of squares is 5.
How to find the percentage of shaded grid?a. Percentage of shaded grid
The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.
Percentage of shaded grid = Shaded grid /Total grid
Percentage of shaded grid = 9/20 × 100
Percentage of shaded grid = 45%
b. Number of squares to be shaded
Number of squares = 20 grid × (70% - 45%)
Number of squares = 20 grid × 25%
Number of squares = 5 squares
Therefore the percentage is 45% .
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Claire Russell is buying a car. Her November monthly interest was $210 % interest. What is Claire’s principal balance at the beginning of November? Use 360 days. (Use 360 days. Do not round the denominator in your calculation and round your final answer to the nearest dollar.)
The Claire's principal balance at the beginning of November is 32516.
Given that,
Vehicle purchase by Claire Russell. Her interest rate for the month of November was 210 percent at 7 3/4%. Employ 360 days. When calculating, do not round the numerator; instead, round your result to the nearest dollar.
We have to find how much was left on Claire's principal at the start of November.
We know that,
Principal= Interest / time× rate of interest
Here,
Interest is 210
Time is 30/360
Rate of interest is 0.0775
Principal = 210/(30/360)×0.0775
Principal= 210/ 0.00645833
Principal =32516
Therefore, The Claire's principal balance at the beginning of November is 32516.
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Find the value of x in the equation
4^x+16^x= 272
Answer:
x = 2
Step-by-step explanation:
Mr. Dunston and Mr. Dolland spent $45 all
together. Mr. Dunston and Ms. Campbell
spent $65 all together. If Ms. Campbell spent
3 times as much as Mr. Dolland, how much
did Mr. Dunston spend?
Mr. Dunston spend is $35.
Given:
Mr. Dunston and Mr. Dolland spent $45 all together.
Mr. Dunston and Ms. Campbell spent $65 all together.
If Ms. Campbell spent 3 times as much as Mr. Dolland.
Let x , y , z be spend of dunston ,dolland and campbell.
x + y = 45
x + z = 65
z = 3*y
x + 3y = 65
on substracting x + y = 45 and x + 3y = 65 we get,
x + y - x - 3y = 45 - 65
-2y = -20
2y = 20
y = $10.
substitute y value,
x + 10 = 45
x = 45 - 10
x = $35
Therefore Mr.Dunston spend $35.
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The table shows the population of Center City in various years. Use the data from 1990 and 2005 to create a linear model that predicts the population of the city (y) in a given year (x). In which year was the actual population of Center City most different from the value predicted by this model?
Year
City Population
1985
194,957
1990
197,800
1992
199,532
2000
203,750
2005
206,561
2012
210,600
1985
1992
2000
2012
Answer:
g(x)=−x−5, find g(1)g(1)
Step-by-step explanation:
g(x)=−x−5, find g(1)g(1)
Answer: 2012
Step-by-step explanation: biggest shift in pop
Miriam bought a barbecue grill on sale for 25% off the original price. Including an 8% sales tax, the final cost was $79.95. If Miriam wants to determine the original cost of the grill, what is an equation that she can use to solve the problem if x represents the original price?
The Original price of barbecue grill is 96.325.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The final cost barbecue grill is $79.95.
Discount = 25%
and Tax = 8%
let the original price be x
x- 0.25x + 0.08x = 79.95
0.83x = 79.95
x= 79.95/0.83
x = $96.325
Hence, the Original price of barbecue grill is 96.325.
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Fewer than %97 of adults have a cell phone. In a reputable poll of 1160 adults, % 88
said that they have a cell phone. Find the value of the test statistic
The value of the test statistic of the given problem is; -17.969
How to find the test statistic?
In statistics, hypothesis testing is simply a method used to test a claim about a population.
We are given;
Sample size; n = 1160
Sample proportion; p^ = 88% = 0.88
The percentage of 97% represents the proportion of a population and this tells us that we are making a claim about the population proportion (p) in the hypotheses.
We claim "fewer then 97%", which indicates less than 97% or 0.97:
p<0.97
The null hypothesis states that the population proportion is equal to the value mentioned in the claim.
H₀: p = 0.97
The claim is either the null hypothesis or the alternative hypothesis. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.
Hₐ: p < 0.97
The value of the test-statistic is gotten from the formula;
z = (p^ - p)/(√(p(1 - p)/n))
z = (0.88 - 0.97)/(√(0.97(1 - 0.97)/1160))
z = -17.969
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Write the equation of the line in fully simplified slope-intercept form.
Answer: y = -x - 8
Step-by-step explanation:
Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.
We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).
For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.
Now, we will write the full equation:
y = -x - 8
the data given to the right includes data from 37 candies, and 5 of them are red. the company that makes the candy claims 30% of its candies are red. use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. what do you conclude about the claim of 30%?
The Sample proportion for the data to construct a 95% confidence interval is 0.1351.
The percentage of red candies is (24.5%, 2.52%)
What do you mean by sample proportion?
The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Sample proportion [tex]=\frac{5}{37}=0.1351[/tex]
For 95% confidence interval, z = 1.96
Hence,
95% confidence interval will be:
[tex]0.1351 \pm 1.96\times \sqrt{0.1351\times(1-0.1351)/37}[/tex]
[tex]0.1351\pm0.1099[/tex]
(0.245, 0.0252)
(24.5%, 2.52%)
Since the confidence interval only contains values less than 30%.
The result is not consistent with 34% rate reported by the candy maker.
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The equation a = 12850 + 530h gives a hiker's altitude a (in feet), h hours after beginning his hike.
A. At what rate, in feet per hour, is the hiker gaining altitude?
The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
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Find the value of x .. assume that segments that appear to be tangent are tangent .
We got x = 16.54 by using Pythagorean theorem .
What is the Pythagorean theorem in plain English?
According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90° .
18² = 7.1² + x²
324 = 50.41 + x²
x² = 324 - 50.41
= 273.59
x = √ 273.59
x = 16.54
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Calculate the volume of each of the following prisms.
1)
length = 35
width = 14
height = 24
2)
length = 27
width = 14
height = 21
3)
length = 21
width = 21
Height = 21
Step-by-step explanation:
1.) The first shape is a parallelogram like prism, So we use Area of prism= Area of base shape*height
that is, Area of base shape= rectangle,L*B
35*14=490*height
490*24=11760 cm3
2.)A rectangle base prism,
Area of prism= Area of base shape*height
Area of Base shape=27*14
378cm2*21
7938cm3
3.)Square based prism,
Area of prism= Area of base shape*height
=21*21*21 (since all sides are the same)
=9261cm3
What is the simplest fraction equal to 9%?
-10b+3 ≤-37
Compound inequalities
3. Simplify the expression.
(3-i)-(2+6i)
01-7i
0-1+7i
0-6i
05+ Si
Answer:(3-i) - (2 +6i)
Combine like terms:
3-2 = 1
-i - 6i = -7i
Combine to get 1 -7i
Step-by-step explanation:
i’m stuck on c and e
Joe Wong, owner of Cookie Palace, is discussing with his accountant which method of depreciation would be best for his new delivery truck. The cost of the truck is $20,000 with an estimated life of four years. The residual value of the truck is $2,500. Calculate depreciation expenses for each year. (Enter your answers as a whole dollar amount.)
The depreciation expense for each year to the new delivery truck purchased by Cookie Palace would be $4, 375.
How to find depreciation?When given the residual value, depreciation can be found using the straight - line method which has the formula:
= (Cost of delivery truck - residual value) / Number of years in estimated life
Solving for the depreciation expenses each year gives:
= (20, 000 - 2, 500) / 4
= 17, 500 / 4
= $4, 375
In conclusion, the depreciation to the delivery truck every year would be $4, 375.
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To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18
minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8.
Answer:
8 people=24 minutes
Step-by-step explanation:
(1,10)(5,18)=18-10/5-1= 8/4 =2
y-8=2(x-4)
I need help with this problem. Please and thank you.
The correct option; B. Two irrational numbers, are the two roots found for the given quadratic equation.
What is defined as the discriminant?In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its categorization or solution. The discriminant for the quadratic equation ax² + bx + c = 0 is b² - 4ac.If the discriminant is positive, the roots of such a quadratic or cubic equation having real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots have included a conjugate pair of complex roots.For the given question;
The quadratic equation is give as;
x² + 5x + 3 = 0
discriminant D = b² - 4ac
b = 5, a = 1 and c = 3
D = 25 - 4(1)(3)
D = 25 - 12
D = 13
√D = √13
As, number is real, there will be two real roots.
As, root of discriminant √D = √13 is a irrational number, the solutions of the given quadratic equation will be two irrational number.
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Find sin 2x, cos 2x, and tan 2x from the given information.
tan x=-1/5
sin 2x =
cos 2x =
tan 2x =
The values of the different trigonometric functions are as follows:
2x = -5/13Cos 2x = 12/13Tan 2x = -5/12.What is trigonometry?The study of relationships between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations.Now, solve using trigonometry as follows:
tan x=-1/5Now, we have:
sin 2x= (2tan x)/(1 + tan²x)=2*-1/5/(1+(-1/5)²)=-2/5(1+1/25)=-2/5/(26/25)=-2/5*25/26=-10/26=-5/13Then, calculate as follows:
cos 2x= (1 - tan²x)/(1 + tan²x)=(1-(-1/5)²)/(1+(-1/5)²)=(1-1/25)/(1+1/25)=24/25/26/25=24/25*25/26=24/26=12/13Now, we obtain:
tan 2x= 2tan x/(1-tan² x)=2*-1/5/(1-(-1/5)²)=-2/5/(1-1/25)=-2/5/24/25=-2/5*25/24=-10/24=-5/12Therefore, the values of the different trigonometric functions are as follows:
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Answer the questions
(1) 150 cola cans and 260 fruit juice cans need to be stacked in a school canteen. If each stack is
to be of the same height and is to contain cans of the same type, what would be the greatest
number of cans each stack can have?
The greatest number of cans each stack can have is 10.
What is Greatest Common Divisor (GCD)?
The number that divides two or more numbers most precisely by itself is said to be the greatest common divisor (GCD) of those numbers. It is also defined as the highest common factor (HCF).
If a and b are two numbers then the greatest common divisor of both numbers is denoted by GCD(a, b).
Given, Total number of cola cans = 150
Total number of fruit juice cans = 260
According to the question condition, we need to find GCD (150,260)
Now, the prime factorization of 150 and 260 are:
150= 2 x 3 x 5 x 5
260 = 2 x 2 x 5 x 13
So, common factor = 2 x 5 = 10
Then, GCD (150,260) = 10
Hence, the greatest number of cans in each stack can have 10.
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graph: y = |x+2| + 1
Ralph wants to join a travel soccer team, a discretionary expense. His parents tell him he must get a job to earn the money to cover the costs. Ralph now views this discretionary expense as an
essential expense since he must pay his parents back. The costs of the travel team are listed below.
Find the total cost of being on the team.
If Ralph takes a summer job and works 10 weeks over the summer, how much must be average each week to cover the travel team expenses?
If Ralph is paid at a flat rate of exactly q dollars each week, what is the standard deviation of the distribution of his 10 weekly paychecks?
The total cost to be in the team will be $1192. He must earn an average of $119.2 per week for 10 weeks. If Ralph is paid at a flat rate of exactly q dollars each week, so the standard deviation will $0.
What is total cost?Total cost is the sum of all expenditures made to produce a certain level of output; when this total cost is divided by the quantity produced, average or unit cost is discovered. The sum of the fixed and variable costs is the total cost. For instance, if a company has a fixed cost per unit of $30 and a variable cost per unit of $5 that increases as output increases, the total cost will be $35. Total cost is equal to the sum of all fixed and variable costs. Total Cost = (Average Fixed Cost + Average Variable Cost) x Number of Units is another way to express it. All of this had to do with the total cost formula, which is a crucial idea for figuring out the total cost of production.
Here,
The expenses of team is,
Uniform=$67.00
Registration=$50.00
Tournaments=$775.00
Travel =$300.00
Total cost=sum of all expense
=67+50+775+300
=$1192
Average cost=Total cost/number of weeks he worked
=1192/10
=$119.2
Deviation of distribution cost,
If Ralph is paid at a flat rate of exactly q dollars each week then there will be $0 deviation.
It will cost $1192 in total to join the team. For ten weeks, he must make an average of $119.2 per week. If Ralph receives a fixed weekly salary of exactly q dollars, the standard deviation will be zero.
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DD.1 alculate mean, median, mode, and range What is the mean? If the answer is a decimal, round it to the nearest tenth. 45 46 43 41 43
Answer:
The answer to your question is,
MEAN = 43.6
MEDIAN = 43
MODE = 43
RANGE = 5
Step-by-step explanation:
BC I know math :)
A cuboid box has a square base and a height of 0.8 m, as shown in the diagram below. If
the volume of the box is 0.288 m3
, calculate the total surface area of the box.
Answer:
c
Step-by-step explanation:
because the explanation its just c
If [tex]y = \frac{(1 + x)u}{(1 + x)v} [/tex]
Find dy/dx
The value of dy/dx is ( v du/dx - u dv/dx)/v²
From the question, we have
y = (1+x)u/(1+x)v
y = u/v
dy/dx = d/dx(u/v)
d/dx(u/v) = ( v du/dx - u dv/dx)/v²
Derivatives:
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.
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