First, multiply both sides by 10:
[tex]2.8\colon6.4\rightarrow28\colon64[/tex]And divide both sides by 4:
[tex]28\colon64\rightarrow\frac{28}{4}\colon\frac{64}{4}\rightarrow7\colon16[/tex]This way, the simplified ratio is:
[tex]7\colon16[/tex]A building cast a shadow that is 245 ft. in length. If the distance from theshadow to the top of the building is 250 ft, How tall is the building?
You have the next situation:
As the building and its shadow form a angle of 90º (right angle), you use the Pythagoras theorem:
[tex]x=\sqrt[]{h^2-s^2}[/tex]The measure of x is equal to the square root of hypothenusa squared less the shadow measure squared:
[tex]\begin{gathered} x=\sqrt[]{(250ft)^2-(245ft)^2} \\ x=\sqrt[]{62500ft^2-60025ft^2} \\ x=\sqrt[]{2475ft^2} \\ x=49.749ft\approx49.7ft \end{gathered}[/tex]Then, the building is 49.7 feet talldescribe the key features of g(x), including theend behavior, y-intercept, and zeros.g(x) = x^3 - x^2- 4x + 4 than create a graph of the polynomial function
End behavior: You have the leading coefficient (number write in front of the variable with the largest exponent) of +1 and the polynomial degree is odd (3).
For this features the end behavior is: falls to left and rises to right.Y-intercept: The value of g(x) when it cross the y-axis (when x is 0)
Substitute the x in the equation by 0 and evaluate the function:
[tex]\begin{gathered} g(0)=0^3-0^2-4(0)+4 \\ g(0)=4 \end{gathered}[/tex]y-intercept: 4To find the zeros:
Equals the function to 0
[tex]x^3-x^2-4x+4=0[/tex]Factor:
-Factor x²
[tex]x^2(x-1)-4x+4=0[/tex]-Factor -4:
[tex]x^2(x-1)-4(x-1)=0[/tex]-Factor (x-1):
[tex](x-1)(x^2-4)=0[/tex]Write the second factor as a substraction of squares:
[tex]\begin{gathered} (x-1)(x^2-2^2)=0 \\ \\ a^2-b^2=(a+b)(a+b) \\ \\ (x-1)(x+2)(x-2)=0 \end{gathered}[/tex]Equal each factor to 0 and solve x:
[tex]\begin{gathered} x-1=0 \\ x=1 \\ \\ x+2=0 \\ x=-2 \\ \\ x-2=0 \\ x=2 \end{gathered}[/tex]Then, the zeros of g(x) are: x=1, -2, 2mrs. Ruiz planted 14 flowers in three plots she planted 4 flowers in 1 blue pot and split the rest equally between 2 red plots add symbols to the equation below then solve the equation to find the number of flowers mrs. Ruiz planet and each of the two red plots
Total numbers of flowers = 14
4 flowers in the blue pot
Then, 14 - 4 = 10 plants
10 plants were equally planted in 2 red pots.
10 = 2r
r = 5 flowers
Mrs Ruiz planted 4 flowers in the blue pot and 5 flowers in each of the red pots.
NEED HELP ASAP!!! The table shows the relationship between the number of bracelets made and the number of beads used:Number of bracelets Number of beads3 215 357 ?9 63The number of beads used to make 7 bracelets is _______.
49
1) Since this is a proportional relationship, we can fill in the table noticing the factor of proportionality is the same for every row
3 | 21
5 | 35
7 | 49
9 | 63
2) As we can see the factor is 7. So the number of beads used to make 7 bracelets is 49
Can you please help me complete. I am reviewing for a final
Given:
Kayakers pulling a raft. One kayaker pulls with a force of F1=(190, 160) and the other kayaker pause with a force of F2=(128, -121)
Required:
We need to find the angle between F1 and F2
Explanation:
[tex]undefined[/tex]b.) What does the point (2.1, 18.6) represent? Select]
Based on the information of the graph, you can notice that the point (2.1 , 18.6) corresponds to point B.
The point (2.1 , 18.6) means that for 2.1 free throw attemps per game, there are approximately 18.6 points per game.
1500.000 to the nearest hundredth
1500.000 to the nearest hundredth is 1500.00
Given that there is a zero in the thousandths position, the zero in the hundredths position is rounded to zero.
Martina purchased a prepaid card for $30. Long distance calls cost 11 cents a minute using this card. Martina used her card only once to .ake a long distance call. If the remaining credit on her card is $28.46, how many minutes did her call last.
we get that
[tex]\begin{gathered} 28.46+0.11t=30 \\ t=\frac{30-28.46}{0.11}=14 \end{gathered}[/tex]so her call last 14 minutes
5.How much of a 30% solution would you need to make 50 mL of a 2% solution?
Answer:
The quantity of a 30% solution you would need to make 50 mL of a 2% solution is;
[tex]3.33\text{ mL}[/tex]Explanation:
Let x represent the quantity of a 30% solution you would need to make 50 mL of a 2% solution.
[tex]\begin{gathered} 30\text{\% of }x=2\text{\% of 50 mL} \\ 0.3\times x=0.02\times50\text{ mL} \\ x=\frac{0.02\times50\text{ mL}}{0.3} \\ x=3.33\text{ mL} \end{gathered}[/tex]Therefore, the quantity of a 30% solution you would need to make 50 mL of a 2% solution is;
[tex]3.33\text{ mL}[/tex]Five students measured the mass of the rock. Their readings were 95.1g, 97.0g, 96.2g, 96.5g, and 96.7g. Find the mean and median of these measures.
To get the mean of a set of data, the steps are to add all the data and divide by the total number of data.
[tex]\bar{x}=\frac{95.1+97.0+96.2+96.5+96.7}{5}[/tex]Then, solve.
[tex]\bar{x}=\frac{481.5}{5}=96.3[/tex]The mean is 96.3 grams.
On the other hand, the median of a set of data is the middlemost data once the data has been arranged from lowest to highest or vice versa.
Let's arrange the data first.
[tex]95.1,96.2,96.5,96.7,97.0[/tex]Out of the 5 data, the middlemost data would be the third one. Hence, the median is 96.5 grams.
If a submarine is 80 m below sea level if it dives another 15 m, how far below sea level is the submarine now?
ANSWER
EXPLANATION
The submarine is initially 80 m below sea level.
It then dives another 15 m.
That means it goes 15 m lower than its original position.
Sea level is equivalent to 0 m.
Therefore, the submarine being initially 80 m below sea level means that it was at -80 m.
Now, it goes 15 m lower,
whats 9 9/35- 6 8/10
You have the following expression:
9 9/35 - 6 8/10
In order to simplify the prevous expression, first convert the mixed number to normal fractions, just as follow:
9 9/35 = 9/1 + 9/35 = (315 + 9)/(35) = 324/35
6 8/10 = 6/1 + 8/10 = (60 + 8)/10 = 68/10 = 34/5
next, subtract the previous result:
324/35 - 34/5
multiply the second fraction by 7/7 to obtain two homogeneus fractions:
(34/5)(7/7) = 238/35
then, you have
324/35 - 34/5
= 324/35 - 238/35
= (324 - 238)/35
= 86/35
Hence, the simplied expression is 86/35
Answer:
For decimals, it is: 2.45714285714
For fractions, it is: [tex]2\frac{22857142857}{50000000000}[/tex]
Step-by-step explanation:
Please brainliest.
The formula gives the volume V of a right cylinder with radius r and height h.V = πr²hSolve for r
The formula that gives the volume V of a right cylinder with radius r and height h is presented below:
[tex]V=\pi r^2h[/tex]Step 1: Divide both sides by πh
[tex]\begin{gathered} \frac{V}{\pi h}=\frac{\pi r^2h}{\pi h} \\ r^2=\frac{V}{\pi h} \end{gathered}[/tex]Step 2: Take the square root of both sides.
[tex]\begin{gathered} \sqrt[]{r^2}=\sqrt[]{\frac{V}{\pi h}} \\ r=\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]Step 3: We can multiply both the numerator and denominator by πh to get:
[tex]\begin{gathered} r=\sqrt[]{\frac{V\pi h}{\pi^2h^2}} \\ =\frac{\sqrt[]{V\pi h}}{\sqrt[]{\pi^2h^2}} \\ r=\frac{\sqrt[]{V\pi h}}{\pi h} \end{gathered}[/tex]The correct option is the last one.
What is the length of side OR?A:6 unitsB:8 unitsC:10 units D:18 units
The perimeter is the sum of all sides, therefore:
[tex]P=(2x+4)+(x)+(3x+3)[/tex]Since the perimeter is 55 units:
[tex]55=2x+4+x+3x+3[/tex]Add like terms:
[tex]55=6x+7[/tex]Solve for x:
[tex]\begin{gathered} 55-7=6x \\ 48=6x \\ x=\frac{48}{6} \\ x=8 \end{gathered}[/tex]Answer:
x = 8
Using the chart above of 500 people go in for surgery how many are going for eye surgery?
From the graph (a pie chart), we have that the percent of people that go to Eye Surgery is 5%.
We have that total is 500 people. We, therefore, need to get the 5% of 500 to get the number of those that go for eye surgery, then:
[tex]\frac{5}{100}\cdot500\text{ = 25}[/tex]Then, for eye surgery, we have 25 people in total, according to chart.
Sanford's gym coach made him run 20 laps on a 600-m track. How many kilometers did he run? How many miles? Round youranswers to two decimal places, if necessary.wSanford rankilometers, which ismiles.Х5HELP?? Stuck
First, determine how far he ran in meters
20 laps * 600 meters
12000 meters
We can find the number of kilometers by using the conversion factor 1000meters = 1 km
12000meters * 1 km/1000m = 12 km
Now we can convert km to miles
1 km = .62137119 miles
12 km * .62137119 miles/ 1 km
7.45645428
Rounding to 2 decimal places
7.46 miles
which word best describes the degree of overlap between the 2 data sets
Solution
For this case we can see that the best answer is:
Low
Since we have overlap just in some values representing a low percentage of all the datasets
For the second case we have the following dataset:
27 28 28 29 29 29 30 30 30 31 31 31 33 34
We have 14 values then we can find the median like this:
Median = (30+30)/2= 30
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
We have the expressions:
[tex]y>2x+4[/tex][tex]y+x\le6\Rightarrow y\le6-x[/tex]Now, we will graph:
Since it is an intersection, we will graph the values contained by both inequalities.
Answer the questions below using the given scatter plot. a. The scatter plot shows what kind of association?Circle one. Positive, Negative, Noneb. Finish the following sentence.As the number of peaches sold_________,the price of peaches____________.
a) The scatter plot shows a negative association
b) As the number of peaches sold increases, the price of peaches decreases
The formula for the volume of a rectangular prism is V = lwh. What is the formula when solved for w?o202IhW=VwV?hVuw=
Formula for the Volume of rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h; \\ l\text{ is long} \\ w\text{ is width} \\ h\text{ is high} \end{gathered}[/tex]They ask you solve the expresion for w, that means that you have to find a expression like w=?
To do that, you should be move l and w to the other side of equation...
Start moving l,
Tell me, what is doing l to w.. what math operation...
??
Exactly, multiply.. the pass to other side to do the oposite operation.. in this case divide..like this..
[tex]\frac{V}{l}=w\cdot h[/tex]we do the same with h.. and thats all.. then we take:
[tex]\frac{V}{l\cdot h}=w[/tex]or the same
[tex]w=\frac{V}{l\cdot h}[/tex]That's your answer
Find the standard deviation of the data set.**Round your answer to the nearest hundredth.48, 30, 24, 42, 60, 24
Ok, let's find the standard deviation of the data set:
Step 1: calculate the mean.
(48+30+24+42+60+24)/6=228/6=38
Step 2: calculate the square of the distance from the mean for each piece of data.
|48-38|²=10²=100
|30-38|²=8²=64
|24-38|²=14²=196
|42-38|²=4²=16
|60-38|²=22²=484
|24-38|²=14²=196
Step 3: add the values that resulted from step 2.
100+64+196+16+484+196=1056
Step 4: divide by the number of data.
1056/6=176
Step 5: take the square root.
√176≈13.27
Finally we obtain that the standard deviation is 13.27.
Asha has $100 on a movie theatergift card. Each time she buys a ticketto a movie it costs her $8.75. Writean equation that Asha can use to findX, the number of tickets she can buyif she wants to keep a $15 balance onthe gift card.
We can write an equation for the balance of the gift card.
We know that if she doesn't buy any ticket (x = 0), the balance will be $100, which is the initial balance.
Each increase in x, is a decrease of 8.75 for the balance. This represents the slope of the equation, as there is not other term.
Then, we can write the equation as:
[tex]y=100-8.75x[/tex]If she wants to know how many tickets she can buy to have a $15 balance (y = 15), we can use the equation as:
[tex]\begin{gathered} y=15 \\ 100-8.75x=15 \\ 100-15=8.75x \\ 85=8.75x \\ x=\frac{85}{8.75} \\ x\approx9.71 \end{gathered}[/tex]She can buy up to 9 tickets (if she buys 10 tickets, she will have less than $15).
Answer:
The equation is y = 100 - 8.75x.
X = 9 tickets for a balance of $15.
Scott is 72 inches tall. How many feet is Scott? Use a conversion factor to show your work.
Answer
6 feet
Explanation
Note: The conversion rate of inches to feet is given below
1 inches = 0.0833333 foot
Since Scott is 72 inches tall, His height in feet will be
[tex]72\times0.0833333=6\text{ fe}et[/tex]solve the right triangle and round decimal answers to the nearest tenthi know its either option a or c but im not 100% sure which one
Step 1
Name all sides
Hypotanuse = 16 side facing right angle
Opposite = y side facing given angle
Adjacent = x
90 +
Step 2
Find the values of x and y
[tex]\begin{gathered} \theta\text{ = 76} \\ \sin \theta\text{ = }\frac{\text{Opposite}}{\text{Hypotanuse}} \\ \sin 76\text{ = }\frac{y}{16} \\ 0.97\text{ = }\frac{y}{16} \\ \text{Cross multiply} \\ y\text{ = 0.97 x 16} \\ y\text{ = 15.52} \\ y\text{ = 15.5} \end{gathered}[/tex][tex]\begin{gathered} \cos \theta\text{ = }\frac{adjacent}{\text{hypotanuse}} \\ \cos 76\text{ = }\frac{x}{16} \\ 0.24\text{ = }\frac{x}{16} \\ \text{Cross multiply} \\ x\text{ = 0.24 x 16} \\ x\text{ = 3.8}5 \\ x\text{ = 3}.9 \end{gathered}[/tex]Which ordered pair is a solution to the system of equations?Note: Use the substitution method.{x=1/4y+2 and −4x+3y=4 (−1/12, −2/63 )(7/2, 6 )(5/4, 3 )(−1/4, 1 )
Given the system of equations
[tex]\begin{gathered} x=\frac{1}{4}y+2 \\ -4x+3y=4 \end{gathered}[/tex]Substitute x =1/4y+2 in the second equation
[tex]-4(\frac{1}{4}y+2)+3y=4[/tex]Simplify
[tex]\begin{gathered} -y-8+3y=4 \\ 2y-8=4 \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} 2y-8+8=4+8 \\ 2y=12 \\ \frac{2y}{2}=\frac{12}{2} \\ y=6 \end{gathered}[/tex]Then substitute y = 6 in x
[tex]x=\frac{1}{4}(6)+2=\frac{6}{4}+2=\frac{7}{2}[/tex]Answer: (7/2, 6)
if ×=10 what is the value of 2×+5
In order to calculate the value of 2x + 5 if x=10, we would need to substitute in the expression 2x + 5 the variable x with the number 10.
Therefore, 2x + 5 if x=10 would be equal to:
2(10)+5=20+5=25
Therefore, the value of 2×+5 if x=10 would be 25
Activity 1 of 2Mr. Hall needs lights installed in his house and is trying to decide between two electric companies. ABC Electric's charges can be represented by the equation y = 50x + 75 Two Electricians' charges can be represented by the following table: X: 0 1 2 4Y: 70 130 190 250Complete each of the 2 activities for this Task.Which company charges more per hour?Activity 2 of 2Mr. Hall is estimating he needs about 5 hours of work done. Which company should he choose if he is trying to save money? Show your work or explain your reasoning.
1) Two Electricians' charges more per hour
2) Mr Hall should choose ABC electric to save money
Explanation:ABC Electric's charges :
y = 50x + 75
Two Electricians' charges is shown in the table
To determine which company charges more per hour, let's compare their charages
1) y = 50x + 75
when x = 1 hour
y = 50(1) + 75 = 50 + 75
y = $125
From the table, when x = 1
y = $130
$130 > $125
The charge of Two Electricians' for 1 hour is more than that of ABC Electric's charges
Hence, Two Electricians charges more per hour
2) For 5hours, x = 5
inserting the value for x in ABC electric charges:
y = 50(5) + 75
y = 250 + 75
y = $325
There is no value for x = 5 on the table given
we need to find an equation for it
Equation of line: y = mx + c
Rate of change = slope = change in y/change in x
Using points: (0, 70) and (1, 130)
Rate of change = (130-70)/(1-0) = 60/1
Rate of change = slope = 60
The y-intecept is when x = 0
y-intercept = c = 70
equation for Two Electricians' charges :
y = 60x + 70
when x = 5
y = 60(5) + 70
y = 300 70
y = $370
$370 > $325
ABC electric cost less for 5hrs
Mr Hall should choose ABC electric to save money
Gerd is considering an account that earns 6% interest per annum compounded monthly. What is the annual percentage yield (APY)? Give your answer as a percent rounded to the nearest tenth (e.g. 5.1%). Do not include the percentage sign (%) in the answer box below.
Data
Interest = 6%
Annual percentage yield = ?
APY = (1 + r/n)^n -1 12 is because a year has 12 months
6% = 0.06
APY = (1 + 0.06/12) ^12 - 1
APY = (1 + 0.005)^12 - 1
APY = (1.005)^12 - 1
APY = 1.062 - 1
APY = 0.062 or 6.2%
Which expression uses the commutative property to make it easier to evaluate ( – 5). 11. ? 3 5 11 O A. (-). 11 $). O B. (-6).3. OC. . 11.(-5) O D. (-5) 5.11 SUBN
I’m here to help you. Just give me a few mins to look over your question.
Step 01:
Data
(-6/5) *11 * 3/5
Commutative property
Step 02:
We must analyze the expressions to find the solution.
Commutative property
[tex]\frac{5}{3}\cdot11\cdot(-\frac{6}{5})[/tex]That is the solution .
The sum of the three angles of a quadrilateral is 310°, what is the measure of the fourth angle?
The sum of the angles in a quadrilateral is 360 degrees. Let x represent the fouth angle. If the sum of the three angles of the quadrilateral is 310, it means that
310 + x = 360
subtracting 310 from both sides,
310 - 310 + x = 360 - 310
x = 50
the measure of the fourth angle is 50 degrees