we can see that
[tex]\frac{6}{48}=\frac{6}{6\cdot8}=\frac{1}{8}[/tex]hence, the answer is d).
a square box is being cut apart and has a measurement system below. What is the surface area of the box?
ANSWER
73.5 in²
EXPLANATION
To find the surface area, we have to find the area of one face - one of the squares of the diagram - and then multiply that by 6 - because cubes have 6 faces.
The area of one face is:
[tex]A_{\text{face}}=3.5^2in^2=12.25in^2[/tex]The surface area of the box is:
[tex]\begin{gathered} S_{}=6A_{\text{face}} \\ S=6\cdot12.25in^2^{} \\ S=73.5in^2 \end{gathered}[/tex]Salma wants to cover her rectangular patio in cement. The patio measures 6 yd long and 4 yd wide. She knows the area each bag of cement covers, but only in square meters.
Answer:
Finding the area right? If so, it's 24 m^2
graph the equation:
y=-6x+12
Identify if the statement is consistent or inconsistent. If the system is consistent, identify wether the equations are dependent or independent.
The solution of the system is: (9, -6)
If a system has at least one solution, it is said to be consistent.
If a consistent system has exactly one solution, it is independent.
Then, the system is consistent and the equations are independent.
In the Alaskan temperature data set, what is the outlier, if any?5, 12, 14, 19, 19, 21, 25, 29, 33
ANSWER
5
EXPLANATION
We want to find the outlier in the data set given.
An outlier is a data point whose value is abnormal or incoherent with other values in the same data set.
That means that it's value does not tally with the other values in measure.
Therefore, the outlier from the data set is 5.
the shorter leg of a right triangle is 7 m shorter than the longer leg. the hypotenuse is 7 m longer than the longer leg. find the side lengths of the triangle. length of the shorter leg:length of the longer leg:length of the hypotenuse:
Answer:
Explanation:
Let the length of the longer leg = x m
The shorter leg of a right triangle is 7m shorter than the longer leg. therefore:
Length of the shorter leg = (x-7) m
The hypotenuse is 7m longer than the longer leg.
Length of the hypotenuse = (x+7) m
We solve for x using Pythagoras Theorem.
[tex]\text{Hypotenuse}^2=\text{Opposite}^2+\text{Adjacent}^2^{}[/tex]This gives us:
[tex]\begin{gathered} (x+7)^2=x^2+(x-7)^2 \\ (x+7)(x+7)=x^2+(x-7)(x-7) \\ x^2+14x+49=x^2+x^2-14x+49 \\ 2x^2-x^2-14x-14x-49+49=0 \\ x^2-28x=0 \\ x(x-28)=0 \\ x-28=0\text{ or x=0} \\ x=28\text{ meters} \end{gathered}[/tex]Therefore:
• Length of the shorter leg: 28-7 = 21 meters
,• Length of the longer leg: 28 meters
,• Length of the hypotenuse: 28+7 = 35 meters
1.Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg wereused in a procedure. Write an equation that can be used to determine how much ofthe isotope is left after x number of half-lives.2. how much would be left after 70 days ?
2) 5.625 mg will be left
Explanation:1) Half-life = 17.5 days
initial amount of Arsenic-74 = 90 mg
To get the equation, we will use the equation of half-life:
[tex]\begin{gathered} N_t\text{ = N}_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}} \\ where\text{ N}_t\text{ = amount remaining} \\ N_0\text{ = initial amount} \\ t_{\frac{1}{2}\text{ }}\text{ = half-life} \end{gathered}[/tex][tex]N_t\text{ = 90\lparen}\frac{1}{2})^{\frac{t}{17.5}}[/tex]2) we need to find the remaining amount of Arsenic-74 after 70 days
t = 70
[tex]\begin{gathered} N_t=\text{ 90\lparen}\frac{1}{2})^{\frac{70}{17.5}} \\ N_t\text{ = 5.625 mg} \end{gathered}[/tex]So after 70 days, 5.625 mg will be left
In a certain chemical, the ratio of zinc to copper is 4 to 17. A jar of the chemical contains 459 grams of copper. How many grams of zinc does it contain?
pls im begging u bro.
The grams of zinc that the jar contains is 108.
What is ratio?It should be noted that ratio simply means the comparison of one thing with another thing.
In this case, the ratio of zinc to copper is 4 to 17 and a jar of the chemical contains 459 grams of copper.
Let the grams of zinc be x. This will be illustrated as:
4/17 = x/459
Cross multiply
17x = 4 × 459
x = (4 × 459) / 17
x = 108
It has 108 zinc.
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Need help with question 2 related to literal C of question 1
For the given parabola:
Vertices, foci and asymptotes:
Vertices: (-2, 0) and (2, 0)
Foci: (-5.385, 0) and (5.385, 0)
Asymptotes: y = -(5/2)x and y = (5/2)x
Fundamental rectangle and conjugate axis endpoints:
Endpoints: 5 and -5
An inlet pipe on a swimming pool can be used to fill the pool in 20 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 1/3 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
We have the next given information:
- inlet pipe fill rate = 1/20 = 1job/hour
-The drain pipe empty rate = 1/45 job/hour
- The pool is 1/3 filled, then we need to fill 2/3.
If both are open, we have the next combined rate:
Combined rate =1/20 - 1/45 = 25/(20*45) = 25/900=1/36 = 1job/hour
Now,we need yo use the next equation:
rate * time = work done
Set x for time.
Replacing:
1/36 * x = 2/3
Multiply both sides by 36:
[tex]\begin{gathered} \frac{1}{36}*x=\frac{2}{3} \\ 36\left(\frac{1}{36}\right?x=36\ast\frac{2}{3} \\ x=24 \end{gathered}[/tex]Hence, it will take 24 hours to fill the pool
ABC is congruent to DEF.
what is the length of AB and what is angle EDF?
Answer:
10 In the diagram below, DE divides AB and AC proportionally, m∠C = 26°, m∠A = 82°, and DF bisects ∠BDE. The measure of angle DFB is. 1) 36°. 2) 54°. 3) 72°.
Step-by-step explanation:
6. Sarah made a down payment of $2,000 on a car and pays $210 a month.a. Model this situation with an equationb. Create a table with 5 unique points that represents this situationC. If the car costs $17,750, how long will it take for her to pay it off?
Calculate the simple interest earned. Round to the nearest cent.P = $4200, r = 7%, t = 1 year
The simple interest formula is defined as
[tex]\begin{gathered} I=Prt \\ \text{where} \\ P\text{ is the principal amount} \\ r\text{ is the rate converted to decimal} \\ t\text{ is time in years} \end{gathered}[/tex]Given
P = $4,200
r = 7% → 0.07 (converted to decimal)
t = 1 year
Substitute the following values and we get
[tex]\begin{gathered} I=(4200)(0.07)(1) \\ I=294 \end{gathered}[/tex]Therefore, the simple interest earned is $294.
Find -x + 10 subtracted from 0.A. 0B. -x + 10C. x - 10
GIVEN:
We are given the following expression;
[tex]-x+10[/tex]Required;
To find the value of this expression subtracted from 0.
Step-by-step solution;
To subtract the expression from zero, we re-write as follows;
[tex]\begin{gathered} 0-(-x+10) \\ \end{gathered}[/tex]Note at this point that a negative times a negative results in a positive.
That is,
[tex]\begin{gathered} -\times(-)=+ \\ \\ Also; \\ \\ -\times(+)=- \end{gathered}[/tex]Therefore, we simplify as follows;
[tex]\begin{gathered} 0-(-x+10) \\ \\ =0+x-10 \\ \\ =x-10 \end{gathered}[/tex]Therefore, the correct answer is option C
ANSWER:
[tex]C:x-10[/tex]Quadrilateral WXYZ is a rhombus and m∠XWY=u–44°. What is the value of u?
It is given that
[tex]\angle XWY=u-44^o,\text{ and }\angle YZW=110^o[/tex]Recall that the adjacent angles are supplementary in a rhombus.
[tex]\angle XWZand\text{ }\angle YZW\text{ are supplementary angles.}[/tex]The sum of supplementary angles is 180 degrees.
[tex]\angle XWZ+\angle YZW=180^o\text{.}[/tex][tex]Substitute\text{ }\angle YZW=110^o,\text{ we get}[/tex][tex]\angle XWZ+110^o=180^o\text{.}[/tex][tex]\angle XWZ=180^o-110^o[/tex][tex]\angle XWZ=70^o[/tex][tex]\angle XWZ=\angle XWY+\angle YWZ[/tex]Recall that the diagonals bisect the angles of the rhombus.
[tex]\angle XWY=\angle YWZ[/tex][tex]\angle XWZ=\angle XWY+\angle XWY[/tex][tex]\angle XWZ=2\angle XWY[/tex][tex]Substitute\text{ }\angle XWZ=70^o\text{ and }\angle XWY=u-44^o,\text{ we get}[/tex][tex]70^o=2(u-44^0)[/tex][tex]\frac{70^o}{2}=u-44^0[/tex][tex]35^o=u-44^0[/tex][tex]35^o+44^o=u[/tex][tex]u=79^o[/tex]
Hence the value of u=79 degrees.
Solve 3p + 9q = 18 for q
Answer:
[tex]q=2-\frac{1}{3}p[/tex]Explanation:
Given the equation;
[tex]3p+9q=18[/tex]We want to make q the subject of formula;
firstly, let's subtract 3p from both sides;
[tex]\begin{gathered} 3p-3p+9q=18-3p \\ 9q=18-3p \end{gathered}[/tex]Then let us divide both sides by the coefficient of q;
[tex]\begin{gathered} \frac{9q}{9}=\frac{18-3p}{9} \\ q=2-\frac{1}{3}p \end{gathered}[/tex]Therefore, making q the subject of formula;
[tex]q=2-\frac{1}{3}p[/tex]Please need help fast!
Answer:
Slope is [tex]-\frac{7}{2}[/tex] and the y-intercept is (0,-2)
Step-by-step explanation:
First, turn the equation into slope-intercept form.
Slope intercept form is [tex]y=mx+b[/tex]. Where m is the slope and b is the y-intercept
The equation would be [tex]y=\frac{4-7x}{-2}[/tex]. Which is equal to [tex]y=\frac{-7}{2} x-2[/tex].
This means that the slope would be [tex]-\frac{7}{2}[/tex] and the y-intercept is (0,-2)
Below are the times (in days) it takes for a sample of 5 customers from Tony's computer store to pay their invoices.
In this problem, we have the following data sample:
[tex]32,37,24,22,20.[/tex]We must compute the standard deviation of this data sample.
1) First, we compute the mean value which is given by the following formula:
[tex]\bar{x}=\frac{\sum^n_{i\mathop=1}x_i}{n}=\frac{32+37+24+22+20}{5}=\frac{135}{5}=27.[/tex]2) Now, we compute the standard deviation using the following formula:
[tex]\sigma=\sqrt[]{\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})^2}{n-1}}=\sqrt[]{\frac{208}{5-1}}\cong7.21.[/tex]Answer
The standard deviation is 7.21.
B. Write the equation of the best fit line. C. Write the Correlation Coefficient(r).D. What does the Correlation Coefficient(r) mean for this scenario? is there a relationship between the fat grams and the total calories in fast food?
B) For the given values the linear equation which best fit is
[tex]y=11.73x+193.85[/tex]where x correspond to the total fat and y to total calories. The slope m is equal to 11.73 and the y-intercept b is equal to 193.85
C) The correlation coefficient r is equal to 0.97.
D) The relationship is almost linear because r=0.97 which is almost 1. The value r=1 means that both variables fit in a line perfectly.
Josiah can jog 5/6 mile in 15 min find his average speed in miles per hour
Answer:
3 1/3 miles per hourStep-by-step explanation:
Given speed:
5/6 mile per 15 minConvert this to mph as follows:
5/6 mile per 15*1/60 h, since 1 min = 1/60 h5/6 mile per 1/4 h, simplify5/6 : 1/4 mile per 1/4 : 1/4 h, divide both sides by 1/45/6 *4 mile per 1 h, multiply10/3 mile per hour, 3 1/3 miles per hour, convert to mixed fractionAnswer:
10/3 miles per hour
Step-by-step explanation:
Given that,
→ 5/6 mile in 15 min
→ 15 min × 4 = 1 hour
Average speed in miles per hour,
→ 5/6 × 4
→ 20/6
→ 10/3 miles per hour
Hence, required answer is 10/3.
Classify the symmetry of the function shown on the graph below. A) cannot be determined from the graph B) evenC) neither D) odd
The graph of an even function is symmetrical around the x-axis and the graph of an odd function is symmetrical around the origin.
The graph given does not fulfil neither of this conditions, hence we conclude that the function is neither even nor odd; therefore, the answer is C
How many feet are represented by a 4-in. line if it is drawn to ascale of 1/2 in. = 1 ft?
When working with scales, we can find the measures by using the rule of three.
From the scale, we know that 1/2 in corresponds to 1 ft, so, the rule of three is:
1/2 in --- 1ft
4 in --- x
Where "x" is the size of the line in feet repreented by the 4 in line in the drawing.
So, we cross multiply to get the equation:
[tex]\begin{gathered} \frac{1}{2}x=4\cdot1 \\ x=2\cdot4 \\ x=8 \end{gathered}[/tex]Thus, this lines represents a size of 8 ft.
ANSWER PLEASE. FIRST ANSWER WILL BE BRAILIEST!!! DUE TODAY PLEASE HELP!!! WORTH 25 points!!!
The measure of angle C is given as follows:
<C = 80º.
Measure of angle CSegments AD and BE are parallel, hence the angles A and B are congruent, that is, they have the same measure:
<A = <B.
Angle ABE is of 50º, hence the measures of the congruent angles A and B are given as follows:
<A = <B = 50º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the following relation from triangle ABC is established.
<A + <B + <C = 180º.
The measures of angles A and B were already found, hence we can solve for the measure of angle C with the above equation as follows:
<A + <B + <C = 180º.
50 + 50 + <C = 180
<C = 180 - 100
<C = 80º.
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Find the amount and the present value of an annuity of P540 payable every end ofthe month at 7% compounded monthly for 4 years and 5 months.
We have to find the present value of a annuity of $540 payable every end of the month at 7% compounded monthly for 4 years and 5 months.
We can express the present value PV as:
[tex]PV=M\cdot\frac{[1-(1+r\/m)^{-n\cdot m}]}{r\/m}[/tex]where M: monthly payment (M = 540), r: annual nominal rate (r = 0.07), m: number of subperiods of compounding per year (m = 12) and n: number of years (n = 4+5/12).
We can replace the variables with its value and calculate PV as:
[tex]\begin{gathered} PV=540\cdot\frac{[1-(1+\frac{0.07}{12})^{-53}]}{\frac{0.07}{12}} \\ PV\approx540\cdot\frac{[1-(1.005833)^{-53}]}{0.005833} \\ PV\approx540\cdot\frac{1-0.7347}{0.005833} \\ PV\approx540\cdot\frac{0.2653}{0.005833} \\ PV\approx540\cdot45.4826 \\ PV\approx24560.60 \end{gathered}[/tex]Answer: The present value of teh annuity is P 24560.60.
Write the inequality that represents the sentence, "Four less than a number is greater than 49.Choose the correct answer below. A. X+4>49 -B. X-4249C. X-4> 49D. X+4> 49
Let x be the number
Thus, 4 less than a number means
[tex]x-4[/tex]4 less than a number means is greater than 49 means
[tex]x-4>49[/tex]The answer is x-4>49, option C.
Hans is a software salesman. His base salary is $1700, and he makes an additional $70 for every copy of History is Fun he sells. Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 26 coples of History Is Fun.
the equation is:
[tex]P=1700+70N[/tex]so if he sells 26 copies we get that:
[tex]P=1700+26\cdot70=3520[/tex]What is the slope of a line parallel to the line whose equation is 3x-18y=-3783x−18y=−378. Fully simplify your answer.
ANSWER
Slope is 1/6
STEP-BY-STEP EXPLANATION
What to find? The slope of the line parallel to a given equation
Given equation
[tex]3x\text{ - 18y = -378}[/tex]The slope-intercept form of an equation is given below as
[tex]y\text{ = mx + b}[/tex]Where m is the slope of the line
y is the intercept of the y - axis
The next thing is to rewrite the above equation in the format of the slope-intercept equation
[tex]\begin{gathered} 3x\text{ - 18y = -378} \\ \text{ Isolate -18y by substracting 3x from both sides} \\ 3x\text{ - 3x - 18y = -378 - 3x} \\ -\text{ 18y = -3x - 378} \\ \text{Divide through by -18} \\ \frac{-18y}{-18\text{ }}\text{ = }\frac{-3x}{-18}\text{ - }\frac{378}{-18} \\ y\text{ = }\frac{1}{6}x\text{ + 21} \\ y\text{ = }\frac{1}{6}x\text{ + 21} \\ \text{ Since y = mx + b} \\ m\text{ = slope} \\ \text{Hence,m = }\frac{1}{6} \end{gathered}[/tex]For lines that are parallel to each other, the slope remains the same
[tex]m1\text{ = m2}[/tex]Therefore, the slope of the line parallel whose equation is y = 3x - 18y = -378 is 1/6
All of the machines are kept cool by circulating cold water through them. The water makes 1 complete cycle through a 30 foot long tube every 12 seconds. Correctly complete the statement about the distance traveled by the water in 3 minutes and number of complete cycles the water makes in 3 minutes
Fill in the blanks to complete the sentence
The water travels ______ feet and completes _____ cycles in 3 minutes
What is the gcf of 12 and 86?
factors of 12: 1, 2, 3, 4, 6, 12
factors of 86: 1, 2, 43, 86
Then, the greatest common factor (gcf) is 2
what is 288 divided by 16
Answer:
18
Step-by-step explanation:
16x18=288
The solution is, Yes, because the last digit is 8, which is divisible by 4.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
288 divisible by 16
i.e. 288/16 = 18
so, it is divisible.
now, we know that,
because the last digit is 8, which is divisible by 4.
Hence, The solution is, Yes, because the last digit is 8, which is divisible by 4.
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