Answer:
c > 5
Step-by-step explanation:
The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.
ApplicationWe can subtract 3 from both sides to solve this.
c +3 > 8 . . . . . . given
c +3 -3 > 8 -3 . . . . subtract 3 from both sides
c > 5 . . . . . . . . . simplify
The solution is c > 5.
__
Additional comment
Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.
Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.
Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)
As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.
Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
A large high school has 3,000 students.
During a one-week period, 75 students were
selected at random various times of the day.
Each student was asked if he or she had one
or more social media accounts. The survey
found that 3 out of 75 students did not have
any social media accounts. Estimate the
number of students in the entire school who
do not have social media accounts.
Answer:
120 students don't have social media accounts
Step-by-step explanation:
Whether the sample is representative:
Estimate: [tex]\frac{3}{75} (3000)=\frac{9000}{75} =120[/tex]
Hope this helps
plesee help me do I need it under 25min and don't answer if you don't know or else u will be reported thank you (◔‿◔)
Answer:
l = 2.25 cm
Step-by-step explanation:
given l is inversely proportional to w² then the equation relating them is
l = [tex]\frac{k}{w^2}[/tex] ← k is the constant of proportion
(i)
to find k use the condition w = 1.5 , l = 16 , then
16 = [tex]\frac{k}{1.5^2}[/tex] = [tex]\frac{k}{2.25}[/tex] ( multiply both sides by 2.25 )
36 = k
l = [tex]\frac{36}{w^2}[/tex] ← equation of proportion
(ii)
when w = 4 , then
l = [tex]\frac{36}{4^2}[/tex] = [tex]\frac{36}{16}[/tex] = 2.25 cm
The data given to the right includes data from candies, and of them are red. The company that makes the candy claims that % of its candies are red. Use the sample data to construct a % confidence interval estimate of the percentage of red candies. What do you conclude about the claim of %?
Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:
[tex]n = 39, \pi = \frac{8}{39} = 0.2051[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 - 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.0784[/tex][tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051(0.7949)}{39}} = 0.3318[/tex]As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.
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A scientist is tagging fish in the Allentown Lake. She catches a fish, tags it,and releases it back into the water. The scientist knows the exact number of fish in the lake: 32 bass,14 fluke,10 carp, and 3 bull sharks.
Calculate the probabilities that the scientist will catch:
A. a bass and then a carp
B. two consecutive bull sharks
C. a fluke and then any different type of fish
d. a bass, another bass, and a bull shark
Probability has to do with the possibility that an event may or may not happen.
What is the probability?The term probability has to do with the possibility that an event may or may not happen. The value of probability always ranges from zero to one.
Now;
Total number of fishes = 32 + 14 + 10 + 3 = 59
a) probability of catching a bass and then a carp = 32/59 * 10/59 = 320/3481
b) probability of catching two consecutive bull sharks= 3/59 * 3/59 = 9/3481
c) probability of catching a fluke and then any different type of fish 14/59 * (32/59 + 10/59 + 3/59) = 14/59 * 45/59 = 630/3481
d) probability of catching a bass, another bass, and a bull shark = 32/59 * 32/59 * 3/59 = 3072/205379
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A glass inform of frustrum of cone
The volume of the cone illustrated will be 117.2 unit³.
How to illustrate the information?From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.
It should be noted that the volume of a cone is calculated as:
= 1/3 πr²h.
where,
π = 3.142
r = radius = 4cm
h = height = 7cm
In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:
= 1/3πr²h
= 1/3 × 3.14 × 4² × 7
= 117.2 unit³
Therefore, the volume of the shape is 117.2 unit³.
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Complete question:
A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.
Write a linear function that passes through the points (3, -7) and (0, 15)
Answer:
The linear function for the given pts. will be
[tex]y = \frac{ - 22}{3}x + 15[/tex]
Step-by-step explanation:
Hello!
[tex]first \: find \: the \: slope \: for \: the \: two \: pts. \\ m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{(15 - ( - 7))}{(0 - 3)} where \: y2 = 15 \\ y1 = - 7 \\ x2 = 0 \\ x1 = 3 \\ m = \frac{ - 22}{3} \\ thus \: y = mx + b \: \: solve \: for \: b \: using \: one \: of \: the \: two \: points \\ lets \: take \: the \: second \: point \\ y = mx + b \\ 15 = \frac{ - 22}{3} (0) + b \\ b = 15 \\ therefore \: substitute \: this \: value \: to \: get \: the \: \\ y = \frac{ - 22}{3} x + 15[/tex]
5:
will give brainliest
The focal length of the given ellipse is given as (±6, 0)
Equation of an ellipseAn ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.
The standard equation of an ellipse is expressed as;
x^2/a^2 + y^2/b^2 = 1
The formula for calculating the focus of the ellipse is given as:
c^2 = b^2 - a^2
Given the equation of an ellipse
(x-7)^2/64 + (y-5)^2/100 = 1
This can also be expressed as:
(x-7)^2/8^2 + (y-5)^2/10^2 = 1
Comparing with the general equation
a = 8 and b = 10
Substitute
c^2 = 10^2 - 8^2
c^2 = 100 - 64
c^2 = 36
c = 6
Hence the focal length of the given ellipse is given as (±6, 0)
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The letters of "EAGLES" should be evenly spaced across a 70-inch-wide banner, with no margins. Each letter is 10 inches wide. How many inches (x) should exist between each pair of letters
Answer:
2 Inches or ~1.43 Inches
Step-by-step explanation:
2 Inches if it's not including the spacing before the first "E" and after the "S", ~1.43 Inches if it's including the spacing.
You would get 2 Inches since if each letter is 10 inches (total 6 letters), that would be 60 inches. There are 5 total spaces in between all the letters. 70 Inches(Banner size) - 60 Inches (total letter size) = 10 Inches, divided equally within the 5 spaces. That would equal 2 :)
You also get ~1.43 Inches by doing the same process as the one shown above^ (that is if you're including the spacing before and after the word)
:)
The walls of a square room with side length s are being torn down and rebuilt. The area of the new room can be represented by 1.75s(2s + 3).
Which expression represents the area of the new room?
3.75s + 4.75
3.75s2 + 4.75s
3.5s2 + 5.25s
3.5s + 5.25
The expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
How to determine the area of the new room?The given parameters are:
Wall =Square
Length = s
When the wall of the square room is torn down and rebuilt, the area of the new room is represented by 1.75s(2s + 3).
This means that
Area= 1.75s(2s + 3)
Expand the expression
Area= 1.75s * 2s + 1.75s * 3
Evaluate the products
Area= 3.5s^2 + 5.25s
This means that the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
Hence, the expression that represents the area of the new room is (c) 3.5s^2 + 5.25s
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Find x(will give brainlest)
area of regular polygon?
[tex]\huge\purple{Hi!}[/tex]
The area of a regular polygon is one-half the product of its apothem and its perimeter.
Target Costing
Instant Image Inc. manufactures color laser printers. Model J20 presently sells for $460 and has a product cost of $230, as follows:
Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
It is estimated that the competitive selling price for color laser printers of this type will drop to $400 next year. Instant Image has established a target cost to maintain its historical markup percentage on product cost. Engineers have provided the following cost-reduction ideas:
Purchase a plastic printer cover with snap-on assembly, rather than with screws. This will reduce the amount of direct labor by 15 minutes per unit.
Add an inspection step that will add six minutes per unit of direct labor but reduce the materials cost by $20 per unit.
Decrease the cycle time of the injection molding machine from four minutes to three minutes per part. Forty percent of the direct labor and 48% of the factory overhead are related to running injection molding machines.
The direct labor rate is $30 per hour.
a. Determine the target cost for Model J20, assuming that the historical markup on product cost and selling price are maintained.
$fill in the blank 1
per unit
b. Determine the required cost reduction.
$fill in the blank 2
per unit
c. Evaluate the three engineering improvements together to determine if the required cost reduction (drift) can be achieved. Do not round interim calculations but round your final answers to two decimal places.
1. Direct labor reduction $fill in the blank 3
per unit
2. Additional inspection $fill in the blank 4
per unit
3. Injection molding productivity improvement $fill in the blank 5
per unit
Total savings $fill in the blank 6
per unit
a) The target cost for Model J20, assuming that the historical markup on product cost and selling price is maintained, is $200 per unit.
b) The required cost reduction per unit is $30 per unit ($230 - $200).
c) An evaluation of the three engineering improvements together to determine if the required cost reduction (drift) can be achieved as follows:
While the calculated cost reduction, including direct materials, is $25, the required reduction to achieve the target markup cost is $30.
Thus, the expected target cost reduction does not add up with the calculated cost reduction, envisaged by the engineers.
Data and Calculations:Model J20 Selling price per unit = $460
Direct materials $175
Direct labor 40
Factory overhead 15
Total $230
Direct labor rate = $30 per hour
Direct labor rate per minute = $0.50 ($30/60)
Direct labor hours per unit = 1¹/₃ hours ($40/$30) or 80 minutes
Direct labor hours per unit reduction:Normal direct labor time = 80 minutes
Plastic printer cover = -15 minutes
Total new direct labor time = 65 minutes
Direct labor rate per unit = $32.50 ($0.5 x 65)
Additional inspection time = 6 minutes
Injection molding machine = 1 minute
Direct materials cost = $155 ($175 - $20)
Historical markup = 200% ($460/$230 x 100)
Target cost based on historical markup = $200 ($400 x 100/200)
Required cost reduction per unit is $30 per unit ($230 - $200)
1. Direct labor reduction of $7.50 per unit ($40 - $32.50)
2. Additional inspection $3 per unit (6 x $0.50)
3. Injection molding productivity improvement $0.50 per unit
4. Material cost reduction = $20
Total savings are $25 per unit ($7.50 - $3 + $0.50 + $20).
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see attachment for question
The percentage when Potiphar woke up late is 14.4%.
How to calculate the percentage?From the information, it was stated that Potiphar takes a horse and buggy to work everyday. In order to come on time, he must wake up promptly at 6.30am and then hop on the buggy and that anytime he wakes up late or the horse was in traffic, he will be late.
It was further illustrated based on the information given in the question that he was late 24.4% of the time and the horse was in traffic for 10% of the time.
Therefore, the percentage when he woke up late will be gotten by simply subtracting the percentages that we have above. This will be illustrated below:
= 24.4% - 10%
= 14.4%
Therefore, the percentage when Potiphar woke up late is 14.4%.
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What is the value of b?
The value of b as described in the task content by means of solving the two equations simultaneously is; b= -10.
What is the value of b from the given equations?The given simultaneous equations as indicated have been manipulated to determine the value of a which is; 0.5 in the task content.
Hence, by substituting a= 0.5 into the equation; 5 = 30a + b; we have;
5 = 30(0.5) + b
b = 5- 15 = -10.
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2.) A shop sells oranges at 6 for N100. A trader sells the same kind of oranges at 8 for N120.
Which price is cheaper, by how much per orange?
The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.
How is the cheaper price determined?The cheaper price can be computed by finding out the price per unit.
Data and Calculations:Price of Set Unit Price
Sale of 6 oranges N100 N16.67 (N100/6)
Sale of 8 oranges N120 N15.00 (N120/8)
Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.
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Copy the problem, mark the givens in the diagram and write a statement/reason proof
Answer:
Step-by-step explanation:
<E = <T Given
M is the midpoint of TE Given
TM = ME Definition of a midpoint
<TMI = <RME Property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME Corresponding parts of Congruent triangles are Congruent
answer: reasoning:
<E = <T given
M is the midpoint of TE given
TM = ME definition of a midpoint
<TMI = <RME property of Vertically Opposite Angles
ΔTMI = ΔRME ASA = ASA
MI = ME corresponding parts of congruent triangles are Congruent
hope this helps!
La dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once. Find the following probability. The number on the upward face is not 7
Answer:
11/12
Step-by-step explanation:
no of sample space=12
number of 7 to occur is 1/12
number of not 7:
since the total probability is 1
so 1-1/12=11/12
In a field, there are some sheep and some goats. The ratio of sheep to goats is 3:1. If there
are 3 goats, how many sheep are there.
it is that wich is klweijxmpx
Line JM intersects line GK at point N.
Horizontal line G K intersects vertical line J M at point N, forming a right angle. A line extends from point N to L, down and to the right.
Which statements are true about the figure? Select two options.
Angle GNJ is complementary to Angle JNK.
Angle MNL is complementary to Angle KNL.
Angle MNG is complementary to Angle GNJ.
Angle KNJ is supplementary to Angle MNL.
Angle GNM is supplementary to Angle JNK.
The statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK. Option B and E
How to determine the statements
Ray NL creates two angles in the lower right quadrant.
The two angles created form a total of 90°, so the two angles formed are complementary. The relation is given as;
∠MNL + ∠KNL = ∠MNK = 90°
Hence ∠MNL and ∠KNL are complementary
∠GNM and ∠JNK are both right angles (and also vertical angles). They sum up to180°. They can be said to be supplementary.
∠GNM and ∠JNK are supplementary
Thus, the statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK
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Consider the following figure:
Answer:
angle <B = 76
Step-by-step explanation:
The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.
We can write the following equation with this information to find the value of angle <B
<B + 71 = 147 subtract 71 from both sides
<B = 76
Mr. Black bought a television set for $450.00. He later sold the television set at a loss of 30%. (a) Calculate the amount of the loss.
The amount of the loss exists 1350.
What is the amount of loss?
Amount of Loss means an amount equivalent to the outstanding balance of the principal amount, less any amounts recognized by perfecting rights under a security agreement, together with such interest as the executive director shall permit, to a maximum of such interest as may be permitted by rule.
Given: Mr. Black purchased a television set for $450.00. He subsequently sold the television set at a defeat of 30%.
From the given information, we get
[tex]$4500\cdot \frac{30}{100}[/tex]
simplifying, we get
[tex]$4500\cdot \frac{30}{100}[/tex]
= 1350
Therefore, the amount of the loss exists 1350.
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Thirty-two percent of workers in Troberca City are college graduates. You randomly select 50 workers and ask them is he or she is a
college graduate. Find the probability that less than 18 workers are college graduate. (Approximating a Binomial Distribution)
(A) 32.6%
B 67.4%
64.0%
36.0%
The correct option is B) 67.4%
What is the z- score table?A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.
Given here, P(probability that a worker is a college graduate) = 32%
= 0.32
q (probability that a worker is not a college graduate) is 1-0.32 = 0.68
now μ(mean) = n×p
= 50×0.32
= 16
Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]
σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]
σ = 3.2985
now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)
= P(z<0.45)
= 0.674 [using z table]
= 67.4%
Hence option 2 is the correct answer
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please help! just need answers for a and b, please!!!!
The answers are :
a)
A = (0, 1)B = (-1, 0)C = (1, 0)D = (-0.5, 0)b)
E = (-2, -3)Let's find point A by using g(x). A is clearly the y-intercept so take x = 0.
g(0) = 2(0) + 1g(0) = 1A = (0, 1)Points B and C can be found using f(x). As they are the x-intercepts, take y = 0.
0 = 1 - x²x² = 1x = ±1As B lies to the left of the y-axis, its x-coordinate is negative.
B = (-1, 0)As C lies to the right of the y-axis, its x-coordinate is positive.
C = (1, 0)Point D can be found using g(x). D is clearly the x-intercept so take y = 0.
0 = 2x + 12x = -1x = -1/2 = -0.5D = (-0.5, 0)Point E lies at the intersection of f(x) and g(x). So they have to be equated.
f(x) = g(x)1 - x² = 2x + 1x² + 2x = 0x (x + 2) = 0x = -2g(-2) = 2(-2) + 1g(-2) = -4 + 1g(-2) = -3E = (-2, -3)Answer:
see explanation
Step-by-step explanation:
(a)
A lies on the y- axis with x- coordinate of zero
substitute x = 0 into either of f(x) or g(x) for y- coordinate
g(0) = 2(0) + 1 = 0 + 1 = 1
then A (0, 1 )
---------------------
B and C lie on the x- axis with y- coordinate of zero
let f(x) = 0 and solve for x , that is
1 - x² = 0 , then
x² = 1 ( take square root of both sides )
x = ± [tex]\sqrt{1}[/tex] = ± 1
then B (- 1, 0 ) and C (1, 0 )
--------------------------------------
D is the point on the x- axis where g(x) crosses
let g(x) = 0 and solve for x
2x + 1 = 0 ( subtract 1 from both sides )
2x = - 1 ( divide both sides by 2 )
x = - [tex]\frac{1}{2}[/tex]
then D (- [tex]\frac{1}{2}[/tex] , 0 )
-----------------------------
(b)
E is the point of intersection of f(x) and g(x) so equate them, that is
2x + 1 = 1 - x² ( subtract 1 - x² from both sides )
x² + 2x = 0 ← factor out x from each term
x(x + 2) = 0
equate each factor to zero and solve for x
x = 0 ← x- coordinate of A
x + 2 = 0 ⇒ x = - 2 ← x- coordinate of E
substitute x = - 2 into g(x) for corresponding y- coordinate
g(- 2) = 2(- 2) + 1 = - 4 + 1 = - 3
then E (- 2, - 3 )
3. Jessie has 25 small
boxes to put his rock
collection in. He sorts 20
rocks into each box.
How many rocks does
he have in his collection?
Answer:
500 rocks
Step-by-step explanation:
25*20 = 500
HELP ME ,HELP ME ,HELP ME PLEASE.IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
a) 88 degrees
The measure of the central angle is the same as the measure of the arc it intercepts.b) 44 degrees
Angle FEG is inscribed in arc FG, and thus has half the measure of arc FG.Add (x^3 -2x^2+4) + (2x^3+x^2-2) express in standard form
Answer:
3x^3-x^2+0x+2Step-by-step explanation:
add both the equations then you will get
3x^3-x^2+2
but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x
so the equation will be
3x^3-x^2+0x+2
Someone please help me with this question thank youuu
Answer: 148 degrees
Step-by-step explanation:
The total measure of all exterior angles of a convex pentagon is 360 degrees.
If four of them equal 53 degrees then all those together is 212 degrees
53 times 4 = 212
Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!
Hope this helps :)
What would the first step be in solving the equation 4/7x = 21
❄ Hi there,
the first step in solving this inequality is
multiplying (both sides) by 7[tex]\sf{\dfrac{4}{7}x\times7=21\times7}[/tex]. Look what happens on the left side!
[tex]\sf{4x=147}[/tex]
Multiplying both sides of an equation, or inequality, by the fraction's denominator, is a nice little trick when you need to get rid of fractions to solve in terms of a variable.
Finish solving for x by dividing both sides by 4 –
[tex]\sf{x=\dfrac{147}{4}}[/tex]
❄
Solve the differential equation. (x^2 + 11)y' = xy
Separate the variables.
[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]
Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].
[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]
[tex]\ln|y| = \frac12 \ln|u| + C[/tex]
[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]
[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]
[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]
Using separation of variables, the solution to the differential equation is:
y = ksqrt(x² + 11)
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
(x² + 11)y' = xy
Applying separation of variables, we have that:
y'/y = x/(x² + 11)
[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]
[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]
[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]
[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]
Hence the solution is:
y = ksqrt(x² + 11)
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