Step-by-step explanation:
if the solution has "nice" numbers, we can split the expression into 2 factors in the form
(x + a)(x + b) = x² + (a+b)x + ab
as this is equal to x² + 4x - 21.
ab = -21
so, one is positive and one is negative.
and 4 = a + b
we know the typical factors of 21 : 3×7
and then we see easily : 7-3 = 4
so,
we have
(x + 7)(x - 3) >= 0
this has 2 x-intercepts (x-values when y = 0) :
x = -7
x = 3
because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.
that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.
so, the solution are the intervals
x <= -7 and x >= 3
in these areas is the expression x² + 4x - 21 >= 0.
Factorise the following:
27t squared y - 18ty squared
Answer:
9ty(3t - 2y)
Step-by-step explanation:
27t²y - 18ty² ← factor out 9ty from each term
= 9ty(3t - 2y)
Will give brainliest. Please it needs to be correct. Refer to the image
Answer: D
PLEASE GIVE BRAINLIEST THANK YOU!!!
An emperor penguin dive down into the ocean at a contant rate. From the urface, he dive 1,760 feet in 8 minute. The number −1,760 repreent the location of the penguin in relation to the urface. What number repreent the location of the penguin in relation to the urface 2 minute after beginning hi dive?
The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.
First, we will calculate the speed of the penguin. The speed is represented by the variable "s".
s = 1,760/8
s = 220 feet per minute
The location of the penguin after 2 minutes is calculated below.
d = 2×s
d = 2×220
d = 440
Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
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jack paid $99 for 6 pizzas. How much did he pay per pizza?
Answer:
99/6=16.5 per pizza
have u good day
Answer:
16 and a half, ($16.50)
Step-by-step explanation:
99 / 6 = 16.5
Unit 4 congruent triangles
Answer: 9/3
Step-by-step explanation: the trriangles proportion is three and 9/3=3
30 point reward if you help ! find the volume of each shape and then compare. do not reduce your fractions.
The volume of the cuboid is [tex]\frac{6}{125}[/tex] and The volume of the cube is [tex]\frac{8}{27}[/tex]
The comparison of both a cube and a cuboid have six faces,a cube has six faces which are all squares and on the other hand, the cuboid is but a cuboid has rectangular faces.
What is a Cube?
A cube is a symmetrical three-dimensional shape which has all six sides equal.
To find the volume of cube is addition of all seen sides or the given sides all squared.
i.e volume of a cube= [tex]a^{3}[/tex]
volume of the cube=([tex]\frac{2}{3}[/tex])^3
Volume= [tex]\frac{8}{27}[/tex] cubic inches
How to dertermine the volume of a cuboid
Whar is a Cuboid?
A Cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges which the volume can be measured by multiplying the length by the breadth by the height .
Volume of a cuboid = L×B×H
Volume of a cuboid=[tex]\frac{2}{3}[/tex]×[tex]\frac{1}{5}[/tex]×[tex]\frac{3}{5}[/tex]
Volume of a cuboid=[tex]\frac{6}{125}[/tex] cubic inches.
To compare,
A cube has shapes of equal sides six faces and a cuboid faces are non-equal with six faces, 8 vertices and 12 edges.
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Write 10x - 5y = -30 in slopeintercept form.
y =
X +
Answer:
[tex]y=2x+6[/tex]
Step-by-step explanation:
Slope-intercept form is [tex]y=mx+b[/tex].
Therefore, rearranging the given formula:
[tex]10x-5y=-30[/tex]
[tex]-5y=-10x-30[/tex]
[tex]\frac{-5y}{-5}=\frac{-10x}{-5}-\frac{30}{-5}[/tex]
[tex]y=2x-(-6)[/tex]
[tex]y=2x+6[/tex]
Answer: y=2x+6
Step-by-step explanation:
A slope-intercept form is y=mx+b
Hence,
[tex]10x-5y=-30\\\\10x-5y+5y=-30+5y\\\\10x=-30+5y\\\\10x+30=-30+5y+30\\\\10x+30=5y[/tex]
Divide both parts of the equation by 5:
2x+6=y
Thus, y=2x+6
Show that
tan15°=2−√3
It is proved that tan15°=2−√3 by using the identity of tan(A-B)
What are the 3 trignometric identities?
The right-triangle theorem, also known as Pythagoras theorem, is the foundation for the three Pythagorean trigonometric identities.
[tex]sin^{2}a+cos^{2}a=1[/tex]
[tex]1+tan^{2}a=sec^{2}a[/tex]
[tex]cosec^{2}a=1+cot^{2}a[/tex]
The reciprocal trigonometric identities are:
Sin θ = 1/Cosec θ or Cosec θ = 1/Sin θ
Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
Tan θ = 1/Cot θ or Cot θ = 1/Tan θ
tan 15 = tan(45 - 30)
As tan(A - B) = (tanA - tanB)/(1 + tanAtanB)
tan15 = tan(45 - 30) = (tan45 - tan30)/(1 + tan30tan45)
= [tex]\frac{1 - \sqrt{3} }{1+\sqrt{3} }[/tex]
= [tex]\frac{1-\sqrt{3} }{1+\sqrt{3} }[/tex] × [tex]\frac{1 - \sqrt{3} }{1-\sqrt{3} }[/tex]
= [tex]\frac{(1-\sqrt{3}) ^{2} }{1-\sqrt{3} ^{2} }[/tex]
= [tex]\frac{(1-\sqrt{3}) ^{2} }{1-3}[/tex]
= [tex]\frac{(1-\sqrt{3} )^{2} }{-2}[/tex]
= [tex]\frac{1+3-2\sqrt{3} }{-2}[/tex]
= [tex]\frac{4-2\sqrt{3} }{-2}[/tex]
= 2-[tex]\sqrt{3}[/tex]
Hence it is proved that tan15°=2−√3
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a wooden artifact from an ancient tomb contains 25 percent of the carbon-14 that is present in living trees. how long ago, to the nearest year, was the artifact made? (the half-life of carbon-14 is 5730 years.)
The artifact was created 11,460 years ago.
Given
that,25% of the carbon-14 found in living trees can be found in a wooden artifact from an ancient tomb and the half-life of carbon-14 is 5730 years Half Time [tex]t_{1/2}[/tex] = 5730 yearsln 2 / k = 5730k = 5730 / ln 2Let Po = 100P(t) =25 after t yearsP(t) = Po e^ -kt25 = 100 e ^ -(5730t / ln 2)5730t / ln 2 = ln 4
By applying
we get,t = 5730 * log⁴₂t = 11460 years Hence, the artifact was made 11,460 years ago.
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Find the perimeter of a rectangle with a diagonal of 20 inches that make angle measure 30 and 60 using trigonometric function (sine, cosine, tangent)
The perimeter of the rectangle is 20 + 20√3 inches.
How to find the perimeter of a rectangle?The perimeter of a rectangle is sum of the whole side of the rectangle. The side bounded by the rectangle is the perimeter of the rectangle.
Therefore, the diagonal of the rectangle is given as 20 inches.
Using trigonometric ratios, let's find the sides of the rectangle.
sin 30 = opposite / hypotenuse
sin 30 = x / 20
x = 20 sin 30
x = 20 × 0.5
x = 10 inches
Therefore, using Pythagoras theorem,
20² - 10² = b²
b² = 400 - 100
b = √300
b = √100 × 3
b = 10√3
Hence,
perimeter of the rectangle = 2(l + w)
perimeter of the rectangle = 2(10 + 10√3)
perimeter of the rectangle = 20 + 20√3
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1 3/4 divided by 3
Please helppp
Answer:
= 7/12
Step-by-step explanation:
1 3/4 = 1 + 3/4 = 4/4 + 3/4 = (4+3)/4 = 7/4
(7/4)÷3 = 7/(4*3) = 7/12
a scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. in 1990s, the average amount of time spent playing computer games was 10.2 hours per week. is the amount of time greater than that for this year? ten students were surveyed and asked how many hours they spent playing video games. the test statistics is equal to 0.45. what is the p-value?
Using the concepts of the hypothesis test, it is found that the p-value is of 0.0007 corresponding to ten students who were surveyed and asked how many hours they spent playing video games.
At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:
H[tex]_o[/tex] = μ=10.2
At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:
H₁=μ> 10.2
Ten students were surveyed, so there are 9 df. The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value.
Thus, using a t-distribution calculator, the p-value of the test is of 0.0007.
Hence, when the ten students were surveyed and asked how many hours they spent playing video games and the test statistics is equal to 0.45,then the p-value is 0.0007
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pls help! Last year, 180 new houses were built in a neighborhood. So far this year, 5/6 of them have been sold. How many new houses have been sold this year? Write your answer in simplest form.
Answer:
150 Houses
Step-by-step explanation:
180/6=30. Every 1/6 is 30 houses. Therefore you multiply 30x5 to get 150. 150 is 5/6 of the houses sold.
I NEEEDD HELP ASAPP PLEASE
Solve negative three minus one and two fifths.
three fifths
one and two fifths
negative four and two fifths
four and two fifths
Answer:
Step-by-step explanation:
1. Put Words into Math.
Negative three minus one and two fifths= -3- 1 2/5
2. Solve the math problem
-3-1 2/5= -4 2/5 or -22/5 in improper fraction
Answer: -4 2/5 or -22/5
Carrie visited two different pet adoption centers. At the first adoption center, the ratio of dogs to birds was 4:24. The ratio of dogs to birds at the second adoption center was equivalent.
Which is the ratio of dogs to birds at the second adoption center?
The ratio of dogs to birds at the second adoption center that are equivalent is 2:12.
What is a ratio?Ratio demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
At the first adoption center, the ratio of dogs to birds was 4:24. The ratio will be:
= 4 / 24
= 1/6
= 1:6
Since the ratio of dogs to birds at the second adoption center is equivalent, this can be 2 to 12. This will be:
= 2/12.
= 1/6
= 1:6
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A large company releases summary statistics about the annual salaries for its employees. Mean standard deviation minimum Q1 median Q3 maximum $63,429 $38,439 $18,000 $50,000 $58,000 $68,000 $350,000 Based on this information, are there any outliers in the data? Explain your reasoning
Pieces of data such as $18,000 and $350,000 represent outliers in this chart in standard deviation .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high. The standard deviation calculates how much the data vary from the mean value. It is helpful for contrasting data sets that might have the same mean but a different range.In this chart, there are outliers. The main outliers are $18,000 and $350,000. This is because we know the mean or average is $63,423, and therefore values that are too different from this average are considered outliers.
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Pls help, due tomorrow!!!!!
Answer:
try -1 it's easier to get the question answered so it can be turned in
In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
every week roger pays for a movie ticket and a soda out of his allowance. last week, roger's allowance was aa dollars. the cost of his movie ticket was 20\ % of the difference between aa and the cost of his soda, while the cost of his soda was 5\%5% of the difference between aa and the cost of his movie ticket. to the nearest whole percent, what fraction of aa did roger pay for his movie ticket and soda?
Answer:
23%
Step-by-step explanation:
We can create two equations:
\[m = \frac{1}{5}(A - s)\]\[s = \frac{1}{20}(A - m)\]
Substituting we get:
\[m = \frac{1}{5}(A - \frac{1}{20}(A - m))\]which yields:
\[m = \frac{19}{99}A\]
Now we can find s and we get:
\[s = \frac{4}{99}A\]
Since we want to find what fraction of $A$ did Roger pay for his movie ticket and soda, we add $m$ and $s$ to get:
\[\frac{19}{99}A + \frac{4}{99}A \implies \boxed{\text{(D)}\ 23\%}\]
PLEASE HELP 69 POINTS
Triangle A has vertices (−2, 1), (1, 1), and (1, 0).
Which triangle is similar to triangle A?
Responses
Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)
Triangle X with vertices (−2, 2), (1, 2), and (1, 0)
Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)
The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.
Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)
The difference is a scale factor of 2
(−2, 1) * 2 = (−4, 2)
(1, 1) * 2 = (2, 2)
(1, 0) * 2 = (2, 0)
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- Use the rules of measurement to subtract:
123.9 g - 56.041 g
Answer:
67.859 g
Step-by-step explanation:
123.9 g - 56.041 g
= 123.900 g - 56.041 g
= 67.859 g
Answer:
Step-by-step explanation:
67.859
the table below lists probabilities for the corresponding number of girls in three live births. what is the random variable, what are its possible values, and are its values all numerical?
The random variable in given problem is "x" . The possible values of random variable x are 0,1,2 and 3..
All possible values of random variable is numrical in nature.
We have a table to right lists probabilities for the corresponding number of girls in three live births.
from the table we cleary see that the random variable is x which represents the number of girls in three live births.
Random variable is a variable whose value is unknown or a variable which assigns a numerical value to each trials in Sample Space.
Also, we can see in list that the number of girls in three live birth values are 0, 1 ,2 and 3 ( 3 live birth)
So, the possible values of random variable x is 4 i.e., 0, 1, 2 and 3..
From data we get a result that all possible values of random variable and it's probabilities are numrical in nature.
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a cellular telephone tower that is 110 feet tall is placed on top of a mountain that is 1300 feet above sea level. what is the angle (in degrees) of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level? (round your answer to two decimal places.)
The angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 200 feet above sea level will be 87.36 degrees.
What is angle?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates.
Here,
The cell phone tower's peak will be at a height of 1300 + 110 = 1410 feet above sea level.
Assuming that the user of a cell phone is 200 feet above sea level, the distance between them is 1410 feet- 200 feet, or 1210 feet.
The distance between them horizontally is 5 miles, or 5 * 5280, or 26400 feet.
The opposite cathetus is 26400 feet away and the neighboring cathetus is 1210 feet away.
the angle is 87.376 degrees, or tan(angle) = 26400 / 1210 = 21.82
A cell phone user 5 horizontal miles away and 200 feet above sea level will be depressed at an angle of 87.36 degrees from the top of the tower.
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3. the probability distribution shown below represents the number of trips of five nights or more that american adults take per year. (that is, 6% do not take any trips lasting five nights or more, 70% take one trip lasting five nights or more, etc.). number of trips x probability 0 0.06 1 0.70 2 0.20 3 0.03 4 0.01 1.00 (a) is this an example of a discrete or continuous probability distribution? (b) what is the expected value (mean) number of trips taken? (c) what is the standard deviation of the number of trips taken? (d) what is probability that an american will take three or more trips? (e) what is probability that an american will take two or less trips? (f) what is probability that an american will take at least one trip?
The probability distribution is a) discrete, with b) a mean of 1.23, the standard deviation is c) 0.6458, d) the probability that an American will take 3 or more trips is 0.04, e) the probability that an American will take 2 or less trips is 0.96 and, f) the probability to take at least one trip is 0.94
It is given that the probability distribution of the no. of trips an American adult takes that lasts 5 nights or more
x probability
0 0.06
1 0.70
2 0.20
3 0.03
4 0.01
a)
Here we can see that all the values are isolated and there is no continuity between them. The distribution clearly has breaks between them.
Hence, we can say that the distribution is discrete.
b)
The expected value of any probability
E(X) = ∑xp(x)
where,
x is the random variable
p(x) is the probability of the corresponding random variable hence we get
E(X) = 0 × 0.06 + 1 × 0.70 + 2 × 0.20 + 3 × 0.03 + 4 × 0.01
= 0 + 0.7 + 0.4 + 0.09 + 0.04
= 1.23
Hence the expected value is 1.23
c)
The standard deviation is √σ²
Where σ² = variance of the distribution
σ² = E(X²) - {E(X)}²
{E(X)}² = 1.23²
= 1.5129
E(X²) = ∑x²p(x)
= 0 × 0.06 + 1 × 0.70 + 4 × 0.20 + 9 × 0.03 + 16 × 0.01
= 0.7 + 0.8 + 0.27 + 0.16
= 1.93
Therefore,
σ² = 1.93 - 1.5129
= 0.4171
Therefore
σ = 0.6458
d)
The probability to take 3 or more trips is
P(X≥3)
= P(X = 3) + P(X = 4)
= 0.03 + 0.01
= 0.04
e)
The probability of an American taking 2 or less trips is
1 - P(X≥3)
= 1 - 0.04
= 0.96
f)
The probability that an American will take at least one trip is
P(X≥1)
= 1 - P(X = 0)
= 1 - 0.06
= 0.94
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Mason, a hardwood flooring installer, needs to calculate the amount of hardwood flooring needed to cover a floor that’s 3 3/4 yards Wide and 5 1/2 yards Long. How many square yards of hardwood flooring are needed? (Area= Length x Width). A) 20 5/8 B)15 3/8 C)18 3/4 D)16 1/2
A floor that is 3 3/4 yards wide and 5 1/2 yards long requires 20 5/8 square yards of hardwood flooring area.
length = 5 1/2 yd, breadth = 3 3/4 yd.
Make fractions out of both measurements first.
3 3/4 = 3 + 3/4
= 12/4 + 3/4
= 15/4
5 1/2 = 5 + ½
= 10/2 + ½
= 11/2
Area = (15 * 11)/(4 * 2) yd2
Area = 165/8 yd2
They essentially believed that 165/8 = 20 leftover 5 area = 20 5/8 yd2.
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The points P, Q, R and S all lie on the same line segment, in that order, such that the ratio of PQ:QR:RSPQ:QR:RS is equal to 1:3:1.1:3:1. If PS=35,PS=35, find PR.PR.
The distance of PR is 21
Given,
The points P, Q, R and S all lie on the same line segment.
The ratios;
PQ:QR:RS = 1:3:1.
Distance of PS = 35
We have to find the distance of PR.
A line segment is a piece of a straight line that has all of the points on the line contained within and is bounded by two distinct endpoints. A line segment's length is determined by the Euclidean distance that separates its two ends.
Here,
PQ : QR : RS = 1 : 3 : 1.
Now let PQ = x, QR = 3x and RS = x.
Therefore,
PQ + PR + RS = PS.
x + 3x + x = 35
5x = 35
x = 7
Therefore,
PR = 3x
PR = 3 × 7
PR = 21
The distance of PR is 21
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if sec2a is 3 find the value of sina.
By using trigonometry, it can be calculated that
The value of sina is [tex]\pm \frac{1}{\sqrt{3}}[/tex]
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin \theta, \ cos\theta, \ tan \theta, \ cot\theta, \ sec\theta, \ cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}[/tex]
Trigonometry is a very important tool in mathematics.
Here, the trigonometric equation is
sec 2a = 3
cos 2a = [tex]\frac{1}{3}[/tex]
we know,
[tex]1 - cos 2a = 2 sin^2a\\\\1 - \frac{1}{3} = 2sin^2a\\\\2 sin^2a = \frac{2}{3}\\\\sin^2a = \frac{2}{3} \times \frac{1}{2}\\\\sin^2a = \frac{1}{3}\\\\ sina = \pm \frac{1}{\sqrt{3}}[/tex]
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Simplify the following expressions by adding the like terms: 3a² - 2a - 7 + 3a + 4 - 2a² + 9a x² + 6xy + 5y² - 6xy + 2y² 1 2
the physical examination records of the freshmen class of 1935 at university of toronto were examined in 1980 to see whether the freshman's record of bmi at the time of admission to the university were related to their chance of developing coronary heart disease in 1980. this is an example of:
A prospective research of men and women looked at body mass index, waist circumference, and the risk of coronary heart disease.
What is body mass index?Body Mass Index (BMI) is calculated by dividing a person's weight in kilograms (or pounds) by their height in meters squared (or feet). High body fatness may be indicated by a high BMI.BMI does not make a body fat or health diagnosis for a person, but it does screen for weight categories that may cause health issues.Calculate Adult BMI Using This WidgetBy including this widget on your website, anyone can determine their BMI. For the majority of persons, BMI is an accurate indication of body fatness. It is used to check for weight ranges that could cause health issues. The BMI and accompanying weight category are provided by this calculator. Adults who are at least 20 years old should use this calculator.Child and Teen BMI Calculator Widget from the CDCInclude this widget on your webpage. The CDC BMI-for-age growth chart is used to calculate BMI and the related BMI-for-age percentile. From the age of two to nineteen, kids and teenagers can use this calculator.For Schools: The Children's BMI ToolThis spreadsheet can be used by educators, daycare operators, and other experts to calculate BMI forLearn more about bmi here:
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A solon prices bottles of conditioner by the ounce. An 8-ounce bottle of Brand C cost $14. tHe cost of Brand S is represented by the equations y = 1.5x, where y is the total cost for a bottle with x ounces
Store´s B bottle cost less per ounce.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Store A
Cost of a 8-ounce bottle of water: $14
Store B
Cost of bottle: y= 1.5x
Cost per ounce (A)
=$14/ 8
= $1.75per ounce
Cost per ounce (B); $1.5 per ounce
So, $1.75 > $1.5
Hence, Store´s B bottle cost less per ounce.
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