Determine the unit price of 32 oz for $3.29.
[tex]\begin{gathered} \frac{3.29}{32}=0.1028 \\ \approx0.10 \end{gathered}[/tex]Determine the unit price for 24 oz for $2.59.
[tex]\begin{gathered} \frac{2.59}{24}=0.1079 \\ \approx0.11 \end{gathered}[/tex]The unit price of 32 oz for $3.29 is less. So the better buy round is 32 oz for $3.29.
Divide and simplify 7/8 ÷ -13/7
Please help!!!!!!!!!!!
Simplify the expression.Can you help me with this one. I'm stuck at 12^x4 - 15x^2
Simplify the given expression as shown below
[tex]\begin{gathered} 3x(4x^4-5x)=3x*4x^4+3x(-5x)=12x^5+(-15x^2) \\ =12x^5-15x^2 \end{gathered}[/tex]Therefore, the answer is 12x^5-15x^2Which equation represents a line which is parallel to the line y=8x-4?A x+8y=-16B x-8y=-40C y-8x=-1D 8x+y=3
Two parallel lines has the same slope.
The given line:
[tex]y=8x-4[/tex]Is written in the form y=mx+b where m is the slope.
The slope is 8
To find the parallel line you need to write the given options in the form y=mx+b by solving y, as follow:
[tex]\begin{gathered} A \\ x+8y=-16 \\ 8y=-x-16 \\ y=-\frac{1}{8}x-\frac{16}{8} \\ \\ y=-\frac{1}{8}x-2 \end{gathered}[/tex]Slope is -1/8 (it is not parallel to given line)
_______________
[tex]\begin{gathered} B \\ x-8y=-40 \\ -8y=-x-40 \\ y=\frac{-x}{-8}-\frac{40}{-8} \\ \\ y=\frac{1}{8}x+5 \end{gathered}[/tex]Slope is 1/8 (it is not parallel to given line)
________________
[tex]\begin{gathered} C \\ y-8x=-1 \\ y=8x-1 \end{gathered}[/tex]Slope is 8 (It is parallel to given line)___________[tex]\begin{gathered} D \\ 8x+y=3 \\ y=-8x+3 \end{gathered}[/tex]Slope is -8 (it is not parallel to given line)
Then, as given line and line in option C have the same slope (8) they are parallel linesVictoria's speedboat can travel 105 miles upstream against a 4-mph current in the same amount of time it travels 125 miles downstream with a 4-mph current. Find the speed of Victoria's boat.
Recall that:
[tex]\text{ time }=\frac{\text{ distance}}{\text{ speed}}[/tex]Let Victoria's speed be v.
Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.
Hence the time of journey upstream is given by:
[tex]\frac{105}{v-4}[/tex]And the time of journey downstream is given by:
[tex]\frac{125}{v+4}[/tex]Since the time of journey upstream is the same as the time of journey downstream, it follows that:
[tex]\begin{gathered} \frac{105}{v-4}=\frac{125}{v+4} \\ \text{ Divide both sides by }5: \\ \frac{21}{v-4}=\frac{25}{v+4} \\ \text{ Cross-multiplying, we have:} \\ 21(v+4)=25(v-4) \\ \text{ Expanding the expressions, we have:} \\ 21v+84=25v-100 \\ 25v-21v=100+84 \\ 4v=184 \\ v=\frac{184}{4}=46 \end{gathered}[/tex]Therefore, Victoria's speed is 46 mph
What is the quotient in simplest form? State any restrictions on the variable.see image
we have the expression
[tex]\frac{z^2-4}{z-3}\div\frac{z+2}{z^2+z-12}[/tex]Multiply in cross
[tex]\frac{(z^2-4)(z^2+z-12)}{(z-3)(z+2)}[/tex]Simplify
z^2-4=(z+2)(z-2) -----> difference of squares
z^2+z-12=(z+4)(z-3)
substitute in the above expression
[tex]\frac{\mleft(z+2\mright)\mleft(z-2\mright)\mleft(z+4\mright)\mleft(z-3\mright)}{(z-3)(z+2)}[/tex]Simplify
[tex](z-2)(z+4)[/tex]12–23. Tony Ring wants to attend Northeast College. He will need $60,000 4 years from today. Assume Tony’s bank pays 12% interest compounded semiannually. What must Tony deposit today so he will have $60,000 in4 years?
Answer:
See below
Step-by-step explanation:
Period = 1/2 year total 4years = 8 periods
i = interest per period in decimal form = .12/2 = .06
initial deposit = ?
Final value = 60 000
60 000 = ? ( 1 + .06)^8
? = 37644.74
Describe a series of transformations Matt can perform to device if the two windows are congruent
Answer:
the transformation matt can from A
Log z 2 + log 2x
pahelp po
A cone has a radious of 5inches and a height of 10.125inches.What is the volume of the cone in inch rounded to the nearest tenth?
Answer:
264.9 in³
Explanation:
The volume of a cone can be calculated using the following equation:
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]Where π is approximately 3.14, r is the radius of the cone and h is the height.
So, replacing r by 5 in and h by 10.125 in, we get:
[tex]\begin{gathered} V=\frac{3.14\cdot(5)^2\cdot(10.125)}{3} \\ V=\frac{3.14\cdot25\cdot10.125}{3} \\ V=\frac{794.8}{3} \\ V=264.9 \end{gathered}[/tex]Therefore, the volume of the cone is 264.9 in³
What is the equation of the line that passes through the point (5, 0) and has a slope of 6/5?
Answer:
[tex]y=\frac{6}{5}(x-5)[/tex]
Step-by-step explanation:
Use point-slope form.
Danielle earns $36.80 for 4 hours of yardwork. How much does Danielle earn for 10 hours of yardwork?
Given the Frequency Distribution: (SHOW WORK)
Find the:
(A) Range
(B) Mean
(C) Mode
(D) Median
(E) Variance
(F) Standard Deviation of This Sample
The measures of the frequency distribution is;
(A) Range = 7
(B) Mean = 29
(C) Mode = 12
(D) Median = 29
(E) Variance = 7.612
(F) Standard Deviation = 2.759
How to solve frequency distribution?
A) The range of a frequency distribution is;
Range = Highest Value - Lowest Value
Thus;
Range = 32 - 25
Range = 7
B) Mean is expressed as;
x' = ∑fx/∑f
x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]
x' = 928/32
x' = 29
C) Mode is the value with the highest frequency and so in this case;
Mode = 12
D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29
E) Variance = 7.612
F) The standard deviation is;
σ = √Variance
σ = 2.759
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PLS HELP ME WITH THIS
you need to use the y=mx+b
Hello!
What is a slope-intercept line:
[tex]y = mx + b[/tex]
m: slope[tex]slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}[/tex]
y-intercept or point whose x-coordinate is '0'==> value of y-intercept is '-2'
Thus the equation is [tex]y=-\dfrac{2}{3}x-2[/tex]
Hope that helps!
Answer: y=-2/3x-2
Step-by-step explanation:
1) Draw a triangle from one point to the next point.
For this example, I will use (-3,0) and (0,-2).
You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.
2) Find the y-intercept
Looking at the graph, you can find that the y-intercept is (0,-2).
3) Fill in the y=mx+b
y=-2/3x-2
What value is equivalent to (8+2)2 + (6 − 4) × 3?
Answer:
26
Step-by-step explanation:
PEMDAS
8 + 2 = 10
6 - 4 = 2
10 x 2 = 20
2 x 3 = 6
20 + 6 = 26
y+ 4X=0 linear or nonlinear
Answer:
linear
Step-by-step explanation:
y+4x=0
-4x -4x
=y=-4x+0
it is in the y=mx+b form so it is linear
I only need the answer
THANK YOU!!
Answers:
[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}} = -\frac{2\sqrt{5}}{15}\\\\\csc(\theta) = \frac{7}{2}\\\\\sec(\theta) = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\\cot(\theta) = \frac{-3\sqrt{5}}{2}\\\\[/tex]
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Explanation:
We're given that [tex]\sin(\theta) = \frac{2}{7}\\\\[/tex]
Plug that into the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\[/tex] and solve for cosine to find that [tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\[/tex]
I skipped steps in solving so let me know if you need to see them.
Keep in mind that cosine is negative in quadrant 2
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Once you've determined cosine, divide sine over cosine to get tangent
[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)\\\\\tan(\theta) = \frac{2}{7} \div \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = \frac{2}{7} \times -\frac{7}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2*7}{7*3\sqrt{5}}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3\sqrt{5}*\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3*5}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{15}\\\\[/tex]
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To determine cosecant, we apply the reciprocal to sine.
[tex]\sin(\theta) = \frac{2}{7} \to \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{7}{2}\\\\[/tex]
Similarly, secant is the reciprocal of cosine
[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7} \to \sec(\theta) = \frac{1}{\cos(\theta)} = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\[/tex]
Depending on your teacher, rationalizing the denominator may be optional.
Lastly, cotangent is the reciprocal of tangent
[tex]\tan(\theta) = -\frac{2}{3\sqrt{5}}\to \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{-3\sqrt{5}}{2}[/tex]
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Side notes:
Sine and cosecant are the only things positive in Q2
Everything else (cosine, tangent, secant, cotangent) are negative in Q2.
4x - 2y = 8Solve for yy = 4x + 8y = -2x + 4y = 2x - 4y = -x
This question has to do with the change in the subject of the formula.
So we will proceed thus:
[tex]\begin{gathered} 4x-2y=8 \\ \text{Making y the subject of formula will give:} \\ \end{gathered}[/tex][tex]\begin{gathered} 4x-8=2y \\ \text{Divide both sides by 2} \\ \frac{4x-8}{2}=\frac{2y}{2} \\ 2x-4=y \end{gathered}[/tex]The correct answer, therefore, is the third option:
[tex]y=2x-4[/tex]What is the product of
(5+2i) and (-3 - 4i)?
Answer:
-7 - 26i
Step-by-step explanation:
(5+2i)(-3 - 4i)
take this and distribute them to each other
-15 -20i -6i -8i^2
then combine like terms
-15-26i-8i^2
i^2 is always equal to -1, so replace i^2 with -1 in the problem
-15-26i-8(-1)
now solve
-15-26i+8
now combine like terms and you have your answer
-7-26i
You put together allowance money and head toward a distant planet forsome routine experiments on alien life forms. You abduct 12 aliens from thestrange planet, and you capture the internal body temperature of each(harmlessly of course). That data is presented above. Does this species ofaliens have an average internal body temperature less than that of the humanaverage of 98.6°F?
Solution
The mean of the internal body temperature of the 12 abducted aliens is given by;
[tex]\frac{96.8+98.3+97.6+98.5+97.5+97.5+98.5+65.6+95.4+98+97.4}{12}=87.14<98.6[/tex]A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.09.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
The probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333
Let x = number of tornados
n = 14
p = 0.03
There are just two outcomes that can occur in these independent, fixed trials, and the success probability is 0.03
Consequently, we may determine the probability using the binomial distribution.
Here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)
Using Excel:
P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333
Be aware that the default Excel command to find binomial probabilities that are less than or equal is "=BINOMDIST(x, n, p, 1)"
Therefore, 0.9923333 percent of the time there won't be more than 3 tornadoes in a 14-year period.
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If P = 3+5+7+9+...+99 and Q = 7+9+11+13+...+101 are sums of arithmetic sequences, determine which is
greater, P or Q, and by how much.
Answer:
Q is greater than P by 291
Step-by-step explanation:
The terms of these Arithmetic Sequences are odd natural numbers, because their common difference is 2
And, sum of 'n' odd natural numbers starting from 1 = n²
P = 99² - (1) = 9800
Q = 101² - (1 + 3 + 5) = 10192
Q - P = 291
Hi, I need help differentiating using the product rule, thanks
Differentiate using the product rule:
g. We take out the constant:
[tex]4\frac{dy}{dx}\left(x\left(3x-2\right)^5\right)[/tex]So:
[tex]=4\left(\frac{d}{dx}\left(x\right)\left(3x-2\right)^5+\frac{d}{dx}\left(\left(3x-2\right)^5\right)x\right)[/tex]Now
[tex]\begin{gathered} \frac{d}{dx}\left(x\right)=1 \\ \frac{d}{dx}\left(\left(3x-2\right)^5\right)=5(3x-2)^4\cdot\frac{d}{dx}\left(\left(3x-2\right)^5\right)=5\left(3x-2\right)^4\cdot\:3=15\left(3x-2\right)^4 \end{gathered}[/tex]Substituting the derivatives found:
[tex]=4\left(1\cdot\left(3x-2\right)^5+15\left(3x-2\right)^4x\right)[/tex]Simplify:
[tex]=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)[/tex]Answer:
[tex]=4\left(\left(3x-2\right)^5+15x\left(3x-2\right)^4\right)[/tex]how many ways can nine trophies be arranged on a shelf
we know that
There are: 9 ways to put the first trophy.
8 ways to put the second trophy after putting the first one.
7 ways to put the third trophy after putting the second one.
6 ways .............the third one
5 ways --------> the fourth
4 ways------> 5
3 ways -----> 6
2 ways ----> 7
1 ways-----> 8
therefore
n!
where n=9
9!=9*8*7*6*5*4*4*2*1
9!=362,880
the answer is
362,880 waysFind the area of a square with a diagonal that measures 4 square root of 2
Let's draw the figure to better understand the scenario:
Let,
s = the measure of the sides of the square
For us to be able to determine the area, let's first find out the measure of its side.
We will be using the Pythagorean Theorem:
[tex]\text{ a}^2+b^2=c^2[/tex][tex]\text{ s}^2+\text{ s}^2=(4\sqrt[]{2})^2[/tex][tex]\text{ 2s}^2=32[/tex][tex]\text{ }\frac{\text{2s}^2}{2}=\frac{32}{2}[/tex][tex]\text{ }\sqrt{\text{s}^2}=\sqrt{16}[/tex][tex]\text{ s = 16}[/tex]Let's now determine the area of the square:
[tex]\text{ Area = s}^2[/tex][tex]\text{ = 4}^2[/tex][tex]\text{Area = 16}[/tex]Therefore, the area of the square is 16.
You pick a card at random, put it back, and then pick another card at random.
4 5 6 7
What is the probability of picking a 7 and then picking an odd number?
Simplify your answer and write it as a fraction or whole number.
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Explanation:
A = probability of picking a 7
A = 1/4 since one card is labeled "7" out of four cards total
B = probability of picking an odd number
B = 2/4 = 1/2 because there are 2 cards that are odd (5 and 7) out of 4 cards total.
C = A*B = probability events A and B happen
C = (1/4)*(1/2)
C = 1/8
This only works when we put the first card back, which means each event is independent.
The function is defined by h(x) = (4 + x)/(- 3 + 3x) Find h(4x) .
Given h(x), find h(4x) as shown below
[tex]h(4x)=\frac{4+(4x)}{-3+3(4x)}=\frac{4+4x}{-3+12x}[/tex]Thus, the expanded form of h(4x) is (4+4x)/(-3+12x)Yvonne wants to use a dissection argument to justify the formula for the area of a circle. She dissects the circle into congruent sectors and reassembles the sectors as a parallelogram-like figure. The diagram below shows the arrangement for a circle dissected into 8 sectors. M Height Base Yvonne knows that as the number of sectors of the circle increases, the reassembled figure becomes closer and closer to an actual parallelogram so that it can be used to determine the area of the circle. Determine the value of each characteristic of the parallelogram in the table below. Select the best value for each characteristic.base of the parallelogram height of the parallelogram area of the parallelogram
Each sector is formed like a triangle with a circle base. The sum of all the bases should be equal to half the length of the circle's circumference, this is calculated with the following expression:
[tex]\text{base}=\frac{2\pi r}{2}=\pi r[/tex]This is the base of the parallelogram.
The height of each triangle is the radius of the circle, therefore:
[tex]\text{height}=r[/tex]The area of the parallelogram is the product of the base and the height.
[tex]\text{Area =}\pi r^2[/tex]So the base is pi*r;
The height is r;
The area is pi*r².
Which of the following expressions is equivalent to 3x(2+5y)
Answer:
[tex]15xy+6x[/tex]
The number of classified documents has increased approximately linear from 8.2 million documents in 2001 to 17. 4 million documents in 2005. let in be the number of documents in millions labeled as classified in the year that is years since 2000 find the equation of the linear model to describe the data
Knowing that
- The number of classified documents has increased linearly.
- In 2001 there were 8.2 million documents.
- In 2005 there were 17.4 million documents.
- The variable "n" represents the number of documents (in millions) labeled as classified.
- The variable "t" represents the number of years since 2000.
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
The slope of a line can be found using this formula:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Where these two points are on the line:
[tex](x_1,y_1),(x_2,y_2)[/tex]In this case, you know these two points:
[tex](1,8.2),(5,17.4)[/tex]Then, you can substitute values into the formula and find the slope of the line:
[tex]m=\frac{17.4-8.2}{5-1}=\frac{9.2}{4}=2.3[/tex]Now you know that the form of the equation is:
[tex]n=2.3t+b[/tex]In order to find "b", you need to:
- Choose one of the points on the line:
[tex]\mleft(1,8.2\mright)[/tex]- Identify the value of each variable. Notice that:
[tex]\begin{gathered} n=8.2 \\ t=2001 \end{gathered}[/tex]- Substitute those values of "n" and "t", and the slope into the equation:
[tex]8.2=2.3(1)+b[/tex]- Solve for "b":
[tex]\begin{gathered} 8.2=2.3+b \\ 8.2-2.3=b \\ b=5.9 \end{gathered}[/tex]Therefore the equation of the Linear Model is:
[tex]n=2.3t+5.9[/tex]Hence, the answer is: Option D.