The solutions to the inequality whose graph is as represented in the attached image are;
A) (-4, 0)C) (0, 0)E) (-2,0)Graphical solution of inequalities.It follows from the task content that the graphical solutions for the inequality are represented on the graph and the points which are solutions for the inequality are to be identified.
Therefore, the points which are solutions for the inequality are points which are located in the shaded region of the graph.
Hence, such points include;
A) (-4, 0)C) (0, 0)E) (-2,0)The answer choices B, D and F represents points on the border line of the inequality graph and since the line is broken, they are not solutions to the inequality.
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A harbour seal dives 35 metres below the ocean's surface. Then it dives down an additional 12 metres Determine the seal's new position relative to the surface of the ocean?
The seal's new position relative to the surface of the ocean is 47 meters below.
How to calculate the value?It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.
In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres
The new position will be;
= -35 - 12
= -47
This implies that it's 47 meters below the ocean surface.
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Each of 7 students reported the number of movies they saw in the past year. Here is what they reported. 14,10,16,15,7,15,18
Find the number of movies that the students saw. If necessary, round your answer to the nearest tenth
The total number of movies that the students saw is 105.
I got the answer by adding all of the values that the students saw. So I add 14,10,16,15...etc. which gives me the total of 105.
Which expressions are equivalent to 4n+5?
Select two correct answers.
5n+4
4n+20
1/4(16n+20)
4+n+5
5+4n
The CDC is investigating if the average blood pressure of the US population is
different from 123. A hypothesis test is conducted which returns a sample mean of
128 and a p-value of 0.0037. What is the appropriate conclusion at the 5%
significance level?
Option B. The appropriate conclusion at the 5% significance level is to Reject the null hypothesis, the population mean is significantly different from 123
How to test the hypothesisH0: mean = 123
H1 : mean ≠ 123
We have the p value of the statistics stated already in the question as p value = 0.0037.
The level is significance that we have been given in the question is 5% = 0.05
We are to test here if the true mean is different from 123.
Hence we would be testing the p value against the significance level.
We can see that P value is < level of significance.
0.0037 < 0.05
Hence we would reject the null hypothesis.
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32/25 fraction as a mixed number
The value of 32/25 as mixed number is 1 7/25
What are mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/7 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
A mixed fraction can be obtained wen there is improper fraction. Improper fraction is a fraction that it's numerator is larger than denominator for example 32/25.
To convert to mixed fraction we find the number of times 25 can go in 32, which is 1 and the remainder is 7
Therefore 32/25 = 1 7/25.
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Fabian has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $387.10. He buys 3 bicycle reflectors for $4.43 each and a pair of bike gloves for $12.36. He plans to spend some or all of the money he has left to buy new biking outfits for $45.81 each. What is the greatest number of outfits Fabian can buy with the money that's left over?
Two mechanics worked on a car. The first mechanic charged $85 per hour, and the second mechanic charged $45 per hour. The
mechanics worked for a combined total of 15 hours, and together they charged a total of $1075. How long did each mechanic work?
The first mechanic worked for 10 hours and second mechanic worked for 5 hours.
Given,
Price of first mechanic service =$85/hr
Price of second mechanic service=$45/hr
Total time they worked together=15 hours
Total combined price charged=$1075
Let
Time spend by first mechanic on work =x
Time spend by second mechanic on work =y
Price charged by first mechanic on total work =85x
Price charged by second mechanic on total work=45y
Equation for total time spend by them together on work can be written as,
[tex]x+y=15.....i\\\\y=15-x[/tex]
Equation for total price charged by them can be written as,
[tex]85x+45y=1075\\[/tex]
Substituting y,
[tex]85x+45(15-x)=1075\\\\85x+675-45x=1075\\\\40x+675=1075\\\\40x=1075-675\\\\40x=400\\\\x=10\\[/tex]
Substituting x in eq.[tex]i[/tex],
[tex]10+y=15\\\\y=15-10\\\\y=5[/tex]
Hence, the first mechanic worked for 10 hours and second mechanic worked for 5 hours.
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Over the last three evenings, Amanda received a total of 63 phone calls at the call center. The third evening, she received 2 times as many calls as the first
evening. The second evening, she received 5 fewer calls than the first evening. How many phone calls did she receive each evening?
68 calls she received in each evening .
What is linear equation ?A straight line equation and equations with a maximum order of one are referred to as "linear equations." The formula for the linear equation can be written as Y = mx + b, where m is the slope of the line, b is the y-intercept, and x and y are the variables. Slopes tell us the direction and steepness of a line. The value of y when x is 0 is referred to as the y-intercept because (0,y) is the point where the line crosses the y-axis.
CalculationLet's say the number of calls on the second night was x.
The first evening was then x+7.
The third evening she received 4x calls.
Add them up to make 109 calls....
x + x+7 + 4x = 109
6x + 7 = 109
6x = 102
x = 17 calls
x+7 = 24 calls
4x = 68 calls
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Pls help need by today
Answer:
use AAA congurency rule
Step-by-step explanation:
angle a=angle f
angle b=angle e
angle c= angle d(a+b+c=180 when the triangle 2 sides are equal that means 3 is also equal)
Find the ordered pair (s,t) that satisfies the system
s/2 + 5t = 3 + 5t
3t - 6s = 9 + 3t
Answer:
There isn't one. There is no solution.
Step-by-step explanation:
There are multiple ways to solve this system, but here's what I did:
Solve the both equations for s:
s/2 + 5t = 3 + 5t ⇒ s = 6
3t - 6s = 9 + 3t ⇒ s = -3/2
Since s cannot equal both 6 and -3/2 at the same time, there is no real solution to this system.
1) While mining, Peter found a large metal bar that contained 33 grams of gold. Peter also
determined that the bar was 73.33% gold. What was the total weight of the metal bar in
grams? Round your answer to the nearest whole number if necessary.
The total weight of the metal bar is 45.002 grams.
Given:
While mining, Peter found a large metal bar that contained 33 grams of gold.
Peter also determined that the bar was 73.33% gold.
73.33% = 33 grams
divide by 73.33 on both sides
73.33%/73.33 = 33/73.33 grams
1% = 0.45002 grams
Multiply on 100 on both sides
1%*100 = 0.45002*100
100% = 45.002 grams.
Therefore the total weight of the metal bar is 45.002 grams.
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Differentiate the function with respect to x.
If the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).
What is meant by differentiation?Differentiation is a process that is applied to a function to determine the rate of change of the function in comparison to the rate of change of the independent variable. The result of differentiating a function is known as its derivative. It gives the slope of the function's graph at each point.Differentiation refers to tailoring instruction to meet the needs of each individual. Whether teachers differentiate content, process, products, or the learning environment, the use of continuous assessment and flexible grouping makes this a successful instructional approach.Let the given function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex]
Differentiating with respect to x, we get
d/dx((2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex])
= sin (2) (d/dx(2[tex]$$x^4[/tex] + 1) [tex]$$x^5[/tex] + d/dx ([tex]$$x^5[/tex]) (2[tex]$$x^4[/tex] + 1)
d/dx (2[tex]$$x^4[/tex] + 1) = 8x³
d/dx ([tex]$$x^5[/tex]) = 5[tex]$$x^4[/tex]
= sin (2) (8x³ + 5[tex]$$x^4[/tex] ( (2[tex]$$x^4[/tex] + 1)
Simplify
= sin (2) (8x³ + 5[tex]$$x^4[/tex] ( (2[tex]$$x^4[/tex] + 1)
= sin (2) (18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]
Therefore, the function be f(x) = (2[tex]$$x^4[/tex] + 1) sin 2[tex]$$x^5[/tex] then by differentiating the equation with respect to x, we get sin (2)(18[tex]$$x^8[/tex] + 5[tex]$$x^4[/tex]).
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Graph the solution of this inequality: 2x - 7 > 3 or 4 -x < -4
The solution for the given inequality has been graphed in detail.
What is linear inequality?A linear inequality can be gives the values for a variable in an interval of numbers.
Given inequalities are as below,
2x - 7 > 3 and 4 - x < -4
They can be simplified as,
2x - 7 > 3
=> 2x > 10
=> x > 5
And,
4 - x < -4
=> x - 4 > 4
=> x > 8
The solution of the given inequality is the intersection of two solutions x > 5 and x > 8, which is x > 8.
This is graphed as follows,
Hence, the given inequality has solution x > 8 which has been graphed.
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Mr. Pinello has 80 colored pencils and 64 markers to divide into containers for his class. He wants each container to have the same number of items. What is the greatest number of containers Mr. Pinello can make if he wants each container to have the same number of colored pencils and the same number of markers? Show your work.
Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.
What is the Greatest Common Factor?
The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.
We have,
The number of coloured pencils Mr. Pinello has = 80.
The number of markers and pencils Mr. Pinello has = 60.
The most containers Mr. Pinello can create to ensure that each one contains an identical amount of coloured pencils and markers.
The GCD of the number of coloured pencils and markers will be the largest number of containers to have the same number of items when the same number of items must be preserved.
Calculating the gcd of and 80 and 64 is:
The greatest common divisor (GCD) of both 80 and 64 is 16.
∴ GCD = 16
Therefore, If Mr. Pinello wants each container to contain the same number of coloured pencils and markers, the most containers he can create is 16.
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AM median CM=5x-2 MB = 3x +12 Find CB
The length of the segment CB in triangle ABC where [tex]\overline{AM}[/tex] is a median line and CM = 5·x - 2, MB = 3·x + 12, CM = MB, is 66 units
What is a median line of a triangle?A median line is a line that is drawn from a vertex of a triangle to the middle of the opposite side such that the it bisects the opposite side.
The parameters are; [tex]\overline{AM}[/tex] = A median line
Length of segment CM = 5·x - 2
Length of segment MB = 3·x + 12
Required; The length of segment CB
The median line [tex]\overline{AM}[/tex] bisects the segment CB
Therefore; CM = MB
CB = CM + MB (Angle addition postulate)
Which gives; 5·x - 2 = 3·x + 12 (substitution property of equality)
5·x - 3·x = 2 + 12 = 142·x = 14
x = 14 ÷ 2 = 7
x = 7CB = CM + MB
CB = (5·x - 2) + (3·x + 12)
Which gives; CB = 8·x + 10
x = 7
CB = 8×7 + 10 = 66
The length of segment CB = 66
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What’s the the anwser?
The solution to the compound inequality is x < 3 and x >6. The graph of the solution is shown.
What is inequality?The relation between two unequal expressions is defined as inequality.
The given inequalities are 3x + 6 < 15 and 2x - 5 >7.
Solve the first inequality:
3x + 6 <15
3x < 15 -6
3x < 9
x < 3
Solve the second inequality:
2x - 5 > 7
2x > 7 + 5
2x > 12
x > 6
Hence, the solution to the compound inequality is x < 3 and x >6.
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HELPPP PLEASE FOR BRIANLEST??
Answer:
[tex]-9,-18,-27,-36[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-9[/tex] and the common difference is [tex]-9[/tex], then each successive term in the sequence is [tex]9[/tex] less than the previous term:
[tex]a_n=-9n[/tex]
Therefore, the first term is [tex]-9[/tex], followed by [tex]-18[/tex], [tex]-27[/tex], and [tex]-36[/tex].
Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip to Country A and Country B. Country A's currency is trading at $1.30 per currency A, and Country B's currency is trading at $1.60 per currency B. She plans to spend more time in Country A, so she wants to have four times as much of currency A as currency B. Set up and solve a system of equations to model this problem, and explain what the answer means in practical terms.
If Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip .The currency needed is 200 euro and 500 pounds.
How to find the currency needed?Formulate an equation
1.30x + 1.60y = 3400
Hence,
x =4y Equation 1
1.30x + 1.60y = 3400 Equation 2
Substitute eq1 into eq2
1.30(4y) + 1.60y = 3400
5.2y +1.60y =3400
6.8y =3400
Divide both side by 6.8y
y =3400/6.8
y = 500
Number of euro
4y where y = 500
4(500)
=2000
Therefore the answer in practical terms is : 2000 euro of European currency and 500 pounds of Britain currency are needed.
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PLS HELP WILL MARK BRAINLYIST
Step-by-step explanation:
the solution to a system of functions (lines or any other form of curve) is the point (or points), where they intersect.
in this case : the point (2, 0)
FYI : if there is no intersection, then there is no solution at all (like with parallel lines).
if the curves fully overlap for at least some distance, then we have infinitely many solutions (at least for real numbers). like for identical lines.
Pls help me need by today
The measure of the line AC is 15√3/2
The measure of the line BC is 15/2
What is a Triangle?Triangle ABC is the display style for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.
One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.
Sin 60⁰=x/15
√3/2=x/15
x=15√3/2
The measure of the line AC is 15√3/2
Cos 60⁰= y/15
1/2=y/15
y=15/2
The measure of the line BC is 15/2
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simplify tana+cota help asap
Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.
In the question given, the trig ratio is
tan a + cot a
We can simplify this as
tan a = sin a / cos a
cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a
Adding both ratios together
tan a + cot a = (sin a / cos a) + (cos a / sin a)
tan a + cot a = (cos a + sin a) / sin a * cos a
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I need help with number 2...
For isosceles triangle RST the measure of angle T is 34 degree
In this question, we have been given a isosceles triangle RST with RS = RT.
So, by isosceles triangle theorem,
angle S = angle T
So, angle T = (3x - 2)°
We know that the sum of all angles of triangle is 180°
∠R + ∠S + ∠T = 180°
9x + 4 + 3x - 2 + 3x - 2 = 180°
15x + 4 - 4 = 180°
15x = 180°
x = 12
So, 3x - 2 = 3(12) - 2
= 34°
Therefore, for triangle RST the measure of angle T is 34 degree
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a fabric designer is mapping out a new design. part of the pattern is formed by a repeating polygon the inital polygon has vertices ( -7, 3), (- 4,6), ( -1, 3) and (-4, 0) The next polygon is a translation of the first along the vector {3, -3}. Which is not a vertex of the image?
Considering the given translation, the vertex that is not part of the image is:
H(3,0).
What are the translations to an image?
The translations to an image are represented as follows:
The vector notation of a translation is given as follows:
{x ± a, y ± a}
In this problem, this notation is:
{3, -3}.
Hence the rule applied to each vertex of the image is:
(x,y) -> (x + 3, y - 3).
The vertices of the original figure are as follows:
( -7, 3), (- 4,6), ( -1, 3) and (-4, 0)
Applying the translation rule, the vertices of the image are given as follows:
(-4, 0), (-1, 3), (2, 0), (-1, -3).
The lone coordinate without a vertex of the image is H(3,0).
Missing InformationThe problem is given by the image at the end of the answer.
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Use point-slope form to write the equation of a line that passes through the
point (20,-10) with slope 13/8.
Answer:
[tex]y+10=\frac{13}{8}(x-20)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
Please Help 25 points
Question 5 (1 point)
What is the area of the figure?
5 cm
11.0 cm
20.0 cm
1 cm
2cm
3 cm
The area of the given figure is 25cm².
Area of rectangle
Area = length x width
Perimeter of rectangle
Perimeter = length + length + width + width
Hence, we have
length = 5cm
width = 5cm
then, by applying the Area of the rectangle, we get
Area = length x width
Area = 5 x 5
= 25cm²
Hence, The area of the given figure is 25cm².
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3. Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers. Calculate Lois’ pay before the tax had been deducted.
Lois’ pay before the tax had been deducted is £660.
Given:
Lois Denominator, a mathematics examiner, receives £514.80 after tax has been deducted at 22% for marking papers.
22% = 514.80
divide by 22 on both sides
22%/22 = 514.80/22
1%= 23.4
= 514.8/0.78
= 5148/10/78/100
= 5148*100/10*78
= 66*100/10
= 66*10
= £660.
Therefore Lois’ pay before the tax had been deducted is £660.
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How can i find the domain
Complete steps to find domain of function is describe below.
What is domain ?Domain is defined as the all input values which satisfy the function or can say all inputs any function have.
Steps to find the domain of function:suppose we have a function f(x) = 6x^2 + 5x - 4
For domain solve it for x
⇒ 6x^2 + 5x - 4
⇒ 6x^2+ 8x - 3x - 4
⇒ 2x(3x + 4)· -1(3x + 4)
⇒ (3x + 4) (2x - 1)
values of x are positive for quadratic equation,
⇒ (3x + 4) (2x - 1)≥0
⇒ x ≥ 1/2 or x ≥ -4/3
These are the domain of function.
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A species of animal that has an initial population of 215 experiences uninhibited growth. The rate of growth is 16.63%. About how long does it take the population to grow to 1134? Round to the nearest tenth.
The exponential growth of 16.63% will take approximately 10.80 years to reach a population of 1134
Exponential FunctionAn exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.
Data;
Initial population = 215rate = 16.63%Final Population - 1134Time = ?f(x) = P(1 + r)ˣ
x = time
Substituting the values
1134 = 215(1 + 0.1663)^ˣ
x = 10.80
It will take approximately 10.8 years to reach a growth of 1134
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Answer: The correct answer is "10.0 years"
Step-by-step explanation:
I took the test
A cube shaped aquarium with a side length of 1.2 meters is full of liquid. A fish swims in the container. What is the probability that the fish is at most 0.5 meters away from the center of the container?
The probability that the fish is at most 0.5 meters away from the center of the container, considering the volume of the cube, is given as follows:
0.0723 = 7.23%.
What is the volume of a cube?The volume of a cube of side length s is given by the side length cubed, that is:
V = s³.
The cube in this problem has a side length of 1.2 meters, hence the volume is given as follows:
V = 1.2³ = 1.728 cubic meters.
Considering only the inner 0.5 meters of the cube, the volume is given as follows:
V = 0.5³ = 0.125 cubic meters.
A probability is given by the division of the number of desired outcomes by the number of total outcomes, hence:
p = 0.125/1.728 = 0.0723 = 7.23%.
(desired volume is of 0.125 m³, total is of 1.728 m³).
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