Explanation
To compute the answer, let us make the unknown number y
Thus
We can represent the given statement as
[tex]y-3=63[/tex]The next step will be to solve for y
[tex]\begin{gathered} add\text{ 3 to both sides} \\ \\ y-3+3=63+3 \\ y=66 \end{gathered}[/tex]Therefore, the number is 66
6 At a 33-foot depth underwater, the pressure is 29.55 pounds per square inch (psi). At a depth of 66 feet, the pressure reaches 44.4 psi. At what rate is the pressure increasing? ur answer on ouatlon for the
To solve the exercise you can apply the following formula:
[tex]rate=\frac{\text{difference in pressure}}{\text{difference in depth}}[/tex]In this case, based on the information given in the exercise, you can identify that:
[tex]\begin{gathered} \text{difference in pressure= (44.4.}-29.55)psi=14.85\text{ psi} \\ \text{difference in dept}=(66-33)ft=33\text{ ft} \end{gathered}[/tex]Substituting values, you get:
[tex]rate=\frac{14.85\text{ ps i}}{33\text{ ft}}=0.45\text{ }\frac{ps\text{ i}}{ft}[/tex]Therefore, The pressure is increasing at 0.45 psi per foot.
When graphing unit rates, the unit rate begins at (0, 0), and then at (1, y). What will the 2nd and third points be? (2, _) and (3, _)
When graphing unit rates, the unit rate begins at (0, 0), and then at (1, y).
So, it will represents a line passes through the given points
The slope of the line will be y
So,
The second point will be ( 2, 2y)
And the third point will be ( 3, 3y)
Which of the following statements are true for the image of a triangle after a dilation that has a scale factor of 5/6
EXPLANATION
Since we have a dilation with a scale factor of 5/6, the appropriate statement is the following:
1st) Each angle has the same measure as its corresponding angle in the preimage. This is true because the dilations don't change the shape.
II. Each has a measure 5/6 the length of its corresponding side in the pre-image.
I need the correct choice and the answer for the box
Given the exponential equation:
[tex]16e^t=98[/tex]A student solved it.
Let's describe and correct the error the student made in solving the exponential equation.
Let's solve the equation.
Apply the following steps:
Step 1.
Divide both sides by 16
[tex]\begin{gathered} \frac{16e^t}{16}=\frac{98}{16} \\ \\ e^t=6.125 \end{gathered}[/tex]Step 2.
Take the natural logarithm of both sides
[tex]\begin{gathered} t\text{ ln\lparen e\rparen=ln\lparen6.125\rparen} \\ \\ \end{gathered}[/tex]Where:
ln(e) = 1
Hence, we have:
[tex]t=1.812[/tex]The student did not convert to the logarithmic form correctly. The solution should be t = 1.812
ANSWER:
A. The student did not convert to the logarithmic form correctly. The solution should be
t = 1.812
Goran rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 92 cents for each mile driven. Goran had to pay $252.82 when he returned the truck. For how many miles did he drive the truck?
Let x be the miles driven, and y be the cost, then we can write the following relationship:
[tex]y=0.92x+20.99[/tex]In our case, we know that the final cost was y=252.82 and we need to find the miles given by x, then, we have
[tex]252.82=0.92x+20.99[/tex]By moving 20.99 to the left hand side, we have
[tex]\begin{gathered} 252.82-20.99=0.92x \\ 231.83=0.92x \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{231.83}{0.92} \\ x=251.98\text{ miles} \end{gathered}[/tex]then, the answer is 251.98 miles
A patient started with a 1 liter bag of IV solution. When the doctor checked in on the patient, the bag contained 0.24 liters of the solution. How much solution had been infused into the patient?
Given,
The quantity of solution intially is 1 litre.
The quantity of solution left after infusion is 0.24 litre.
The quantity of solution had been infused into the patient is,
[tex]\begin{gathered} \text{Solution infused tothe patient = total solution -left solution} \\ =1\text{ litre-0.24 litre} \\ =0.76\text{ litre} \end{gathered}[/tex]Hence, the quantity of solution had been infused into the patient is 0.74
help me, this is so confusing
the following set of numbers, find the mean, median, mode and midrange.
9, 9, 10, 11, 13, 13, 13, 14, 25
Question content area bottom
Part 1
The mean, x, is the sum of the data divided by the number of pieces of data. The formula for calculating the mean is x=
Σx
n, where Σx represents the sum of all the data and n represents the number of pieces of data.
Part 2
First find the sum of all the data, Σx.
Σx
=
9+9+10+11+13+13+13+14+25
=
117117
Part 3
Second, find the number of pieces of data, n.
The number of pieces of data listed is enter your response here.
The mean, median, mode and midrange are 13, 13, 13, 17 respectively.
Define mean, median, mode and midrange.An average is a mean. To calculate the sum, add together all the numbers. After that, divide the total by the quantity of numbers.
The median is a midpoint. The fact that the median is in the middle of the road makes it easy to recall. Put the numbers in ascending order, lowest to largest. If there are odd numbers, find the middle one. Add the middle two numbers together and divide by two if the numbers are even.
The most frequent number in a group of numbers is called the mode.
The midpoint is discovered by arranging the numbers from smallest to largest. To determine the sum, add the two smallest and greatest numbers together. By 2, divide the total.
Given data -
The following set of numbers is 9, 9, 10, 11, 13, 13, 13, 14, 25
Σx = 117
To calculate the mean, we use the formula as
Mean = Σx / n
where n is the number of pieces of data i.e. n=9
Therefore, Mean = 117 / 9
Mean = 13
To calculate the median, we use the formula as
Median = Value of [tex](\frac{n+1}{2})^{th}[/tex] th observation
when n is an odd number
So, Median = 10/2
Median = 5
Here the [tex]5^{th}[/tex] observation is 13
As 13 occurs maximum number of times in the given set of numbers and it has 3 times in the given set
Therefore the mode = 13
To calculate the midrange, we use the formula as,
Midrange = (greatest number + least number) / 2
Here the greatest number is 25 and least number is 9
Therefore midrange = (25+9)/2
midrange = 34/2
midrange = 17
The mean, median, mode and midrange are 13, 13, 13, 17 respectively.
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The vertices of ABCDE are A(-6,0), B(-3,0), C(0, -3), D(-3,-6), and E(-6, -3). Find the vertices of the image after a translation using the rule (x,y) - (x + 9, y-6) and a dilation with a scale factor of 4s centered at the origin.
Vertices of new image: A' = (12, -24)
B' = (24, -24)
C' = (36, -36)
D' = (24, -48)
E = (12, -36)
Explanation:A(-6,0), B(-3,0), C(0, -3), D(-3,-6), and E(-6, -3)
A translation of (x + 9, y-6)
A becomes A'
A' = (-6 + 9, 0 - 6) = (3, -6)
B(-3,0)
B becomes B'
B' = (-3+9, 0 - 6) = B' (6, -6)
C(0, -3)
C becomes C'
C' = (0+9, -3-6) = C' (9, -9)
D(-3,-6)
D becomes D'
D' = (-3+9, -6-6) = (6, -12)
E(-6, -3)
E becomes E'
E' = (-6+9, -3-6) = (3, -9)
A dilation with scale factor of 4, we multiply the cooordinates of the alphabeths with prime with 4.
Vertices of new image:
A' = 4(3, -6) = (12, -24)
B' = 4(6, -6) = (24, -24)
C' = 4(9, -9) = (36, -36)
D' = 4(6, -12) = (24, -48)
E = 4(3, -9) = (12, -36)
How to solve 2(x+7)=-4x+14
Let's solve the following equation
[tex]\begin{gathered} 2x+14=-4x+14 \\ 2x+4x=-14+14 \\ 6x=0 \\ x=0 \end{gathered}[/tex]The answer would be x = 0
A shipment of computers arrived at. a warehouse.If each computers is valued at$995. What is the total value of the shipping?
Total number of computers = 20
Cost per a computer = $995
Total cost of 20 computers = 20 x $995
= $19,900
Find the prime factorization of the following number write any repeated racists using exponents
Prime factorization refers to the process of decomposing a given number into a product of prime numbers that can be repeated or not.
Let's remember that prime numbers are numbers that can only be divided by 1 or itself.v Having this in mind we have that the prime factorization of 66 is:
[tex]66=(2)(3)(11)[/tex]If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie ?
we have that
The probability of seeing a romantic or sci-fi movie is
P=0.203+0.12=0.323
therefore
the probability of seeing anything other than a romantic or sci-fi movie is
P=1-0.323
P=0.677
the answer is option BIn the accompanying diagram of a circle of O …..
the theorem says:
[tex]PA^2=PB\cdot PC[/tex]PB=2
PC=2+6=8
[tex]PA=\sqrt[]{2\cdot8}=\sqrt[]{16}=4[/tex]So the answer is
PA=4
Keith is saving money for a car. He has saved the same amount each year for the past three years, and records how much he has at the end of each year in the table below. (a)What is Keith's unit rate of change of dollars with respect to time; that is, how much does Keith save in one year? The unit rate is dollars per year. (b)Graph the proportional relationship described above, with the x-coordinate representing years, and the y- coordinate representing amount saved in thousands of dollars.
Answer:
(a)$1500 per year.
Explanation:
(a)From the table:
3000-1500=$1500
4500-3000=$1500
This means that every year, Keith adds $1500 to his savings.
The unit rate is $1500 per year.
(b)
If x=number of years; and
y=Amount saved (in thousands of dollars.)
When x=1, y=$1.5
When x=2, y=$3.0=2x1.5
When x=3, y=$4.5=3x1.5
The equation of proportion is therefore:
[tex]y=1.5x[/tex]When x=0, y=0 (0,0)
When x=1, y=1.5 (1, 1.5)
We join the points (0,0) and (1,1.5)
The graph of the proportional relationship is attached below.
A lumber yard has fixed costs of $7259.40 per day and variable costs of $0.07 per board-foot produced. Lumbar sells for $1.87 per board-foot. How many board-feet must be produced and sold daily to break even?
The number of board-feet that must be produced and sold daily to break even is:4033.
How to find the number of board-feet to breakeven?Let the number of board-feet produced per day = x
Let the lumber yard's costs each day be: C =$7259.40+ 0.07x
Let the lumber yard's profits be: P = 1.87x
Let P - C = 0
Hence,
1.87x - ($7259.40 + $0.07x) = 0
1.87x - $7259.40 - 0.07x = 0
Combine like terms
1.8x - $7259.40 = 0
1.8x = $7259.40
Divide both side by 1.8x
x = $7259.40/ 1.8
x = 4033
Therefore the breakeven is 4033.
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Use a venn diagram to represent this problemJar A contains numbers that are less than 26 and evenly divisible by 2, Jar B contains numbers that are less than 20 and evenly divisible by 4.
Given:
Jar A contains numbers that are less than 26 and evenly divisible by 2.
The number less than 6 and divisible by 2 are,
[tex]A=\mleft\lbrace2,4,6,8,10,12,14,16,18,20,22,24\mright\rbrace[/tex]Jar B contains numbers that are less than 20 and evenly divisible by 4.
The set is,
[tex]B=\mleft\lbrace4,8,12,16\mright\rbrace[/tex]The Venn diagram is,
Kim's bank gives your 9% simple interest on her college savings account. Ifshe deposits $700 and leaves it in the account for 6 years, howmuch interest will it earn?
Kodex, this is the solution:
Principal = $ 700
Interest rate = 9% = 0.09
Term = 6 years
Let's calculate the interest, using the simple interest formula, as follows:
Interest = Principal * (Interest rate * Term)
Replacing by the values given to us, we have:
Interest = 700 * (0.09 * 6)
Interest = 700 * 0.54
Interest = 378
After 6 years, Kim will earn $ 378 of interest.
Desmond fabricates a tiny microchip it is square in shape measuring seven. 5 mm on each side draw Desmond’s chip to scale on the grid below
Explanation
To draw the square, we were given a scale
2 units represent 1 mm
Therefore, 7.5mm will be
[tex]2\times7.5\text{ units =15 units}[/tex]So that we will have 15 units on all sides
The red sketch above represents the square with a length of 7.5mm
= O DATA ANALYSIS AND STATISTICS Mean and median of a data set A group of 8 students was asked, "How many hours did you watch television last week?" Here are their responses. 16, 16, 9, 9, 9, 7, 16, 10 Find the median and mean number of hours for these students. If necessary, round your answers to the nearest tenth. (a) Median: hours (b) Mean: hours X Ś ?
Solution:
Given:
[tex]16,16,9,9,9,7,16,10[/tex]The median is the middle term from the data rearranged in rank order.
Rearranging the data;
[tex]7,9,9,9,10,16,16,16[/tex]From the data set, the middle term is 9 and 10.
Since two terms fall in the middle, then the median is the mean of the two terms.
Hence,
[tex]\begin{gathered} Median=\frac{9+10}{2} \\ Median=\frac{19}{2} \\ Median=9.5hours \end{gathered}[/tex]Therefore, to the nearest tenth, the median is 9.5 hours.
The mean is the average of the set of data.
[tex]\begin{gathered} mean=\frac{16+16+9+9+9+7+16+10\:}{8} \\ mean=\frac{92}{8} \\ mean=11.5hours \end{gathered}[/tex]Therefore, to the nearest tenth, the mean is 11.5 hours
Evaluate: sin(30 degrees)cos(60 degrees)=(See attached image to assist with these 2 problems)
According to the figure we need to evaluate the sin(30°) and the cos(60°). Remember the trigonometric relations defined over the rectangle triangles as follows, suppose we have an angle called "alpha"
[tex]\begin{gathered} \sin(\alpha)=\frac{oc}{h}, \\ \\ cos(\alpha)=\frac{ac}{h}, \\ \\ tan(\alpha)=\frac{co}{ca} \\ \\ where\text{ }h:Hypotenuse,\text{ }ac:Adjacent\text{ }cathetus\text{ and }oc:Opposite\text{ }cathetus \end{gathered}[/tex]Now, according to the figure, we have that for the angle of 60 degrees:
[tex]\begin{gathered} h=2x,ac=x,oc=\sqrt{3}x \\ \\ \sin(60°)=\frac{oc}{h}=\frac{\sqrt{3}x}{2x}=\frac{\sqrt{3}}{2} \\ \\ \cos(60^{\circ})=\frac{ac}{h}=\frac{x}{2x}=\frac{1}{2} \end{gathered}[/tex]And for the angle of 30 degrees we get the following
[tex]\begin{gathered} h=2x,oc=x,ac=\sqrt{3}x \\ \\ \sin(30°)=\frac{oc}{h}=\frac{x}{2x}=\frac{1}{2}=\cos(60°) \\ \\ \cos(30^{\circ})=\frac{ac}{h}=\frac{\sqrt{3}x}{2x}=\frac{\sqrt{3}}{2}=\cos(60^{\circ}) \end{gathered}[/tex]So, your answer is: sin(30°)=1/2=cos(60°).
-2-3t=-4t how do i solve for t?
You have the following equation:
2- 3t = -4t
In order to solve the previous equation you proceed as follow:
2- 3t = -4t sum 3t both sides
2 = -4t + 3t simplify
2 = -t multiply by -1 both sides
-2 = t
t = -2
Hence, the dolution for t is t=-2
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer: A 143 degrees because angle 5 is a congruent to angle one
Step-by-step explanation:
fill in the table using the function rule y=3x+5
Fill in the table using the function rule y= 3x + 5
________________________________________
Replace each value of x in the expression
____________________________________
x= -4
y = 3* (-4)+5
= -12 +5
= -7
_______________
x= -2
y = 3* (-2)+5
= -6 +5
= -1
_____________
x= 0
y = 3* (0)+5
= 0 +5
= 5
_____________
x= 2
y = 3* (2)+5
= 6 +5
= 11
______________________________
Answer
_________________________
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Stacy made a square tablecloth with a side length of 3.5 feet. She put lace along each side of the tablecloth.How much lace did Stacy need for the tablecloth?
The side of the square is 3.5 feet
The perimeter is
[tex]4\times3.5=14ft[/tex]Stacy need 14 feet lace
The scale from a square park to a drawing of the park is 5 miles to 1 miles. The actual park has an area of 1,600 m×2 what is the area of the drawing
The user corrected that the scale of a drawing of a park reads: 5 miles to 1 cm , and we know that the park measures 1,600 square meters (user insisted that this measure is given in square meters and not square miles).
So we have to convert the 1600 square meters into miles, knowing that 1 meter is the same as: 0.000621371 miles
then meters square will be equivalents to:
1 m^2 = (0.000621371 mi)^2
then 1600 m^2 = 0.00061776 mi^2
now, since 5 miles are represented by 1 cm, then 25 square miles will be represented by 1 square cm
and therefore 0.00061776 square miles will be the equivalent to:
0.00061776 / 25 cm^2 = 0.000024710 cm^2
So and incredibly small number of square cm.
I still believe that some of the information you gave me are not in meters but in miles. (For example, the park may not be in square meters but in squared miles). The park seems to have the size of a house according to the info.
I understand the problem but I do need help with finding the angle measure
1331166633×644÷8797×5
1. The first thing to do is to carry out the two respective multiplications;
[tex]\begin{gathered} 133116633\times644=85,727,111,652 \\ 8797\times5=43,985 \\ \end{gathered}[/tex]2.Now we divide both results, leaving the first result as a dividend and the shortest result as a divisor.
[tex]\begin{gathered} 85,727,111,652/\text{ 43,985} \\ =1,949,007.881141 \end{gathered}[/tex]Triangle TUV is congruent to Triangle GFE. Solve for x, y and z. What is the perimeter of triangle TUV?
Explanation
Step 1
Two triangles are said to be congruent if they are of the same size and same shape.
so, the measures are equivalent
[tex]\begin{gathered} UV=y=12 \\ TU=x=10 \\ TV=GE=z=15 \end{gathered}[/tex]hence, the perimeter of the triangle TUV is
[tex]\begin{gathered} \text{Perimeter}=\text{side}1+\text{side}2+\text{side}3 \\ \text{replace} \\ P=10+15+12 \\ P=37\text{ ft} \end{gathered}[/tex]so, the answer is 37 ft
I hope this helps you
Write the equation of the parabola in vertex form given the vertex (–2, 3) and point (0, 1).
the equation is
[tex]y=-\frac{1}{2}(x+2)^2+3[/tex]PO Triangle ABC is similar to triangular DEF. What is the value of x?
If triangle ABC is similar to DEF then the ratio between the sides will be a constant so we can get the expression:
[tex]\frac{15}{30}=\frac{x}{36}[/tex]and we solve for x so:
[tex]\begin{gathered} x=\frac{36\cdot15}{30} \\ x=18 \end{gathered}[/tex]