write and solve an inequality to represent the situation
For the equation, y= -x - 4, tell whether it’s graph passes through the first quadrant. Explain how you know.
A.) No; for x<0 the y-values are negative.
B.) Yes; for x>0 some y-values are positive.
C.) No; for x>0 the y-values are negative.
D.) Yes; for x<0 some y-values are positive.
The graph of the equation y = -x - 4 does not pass through the first quadrant because for x < 0, the y-values are negative.
Explanation:The given equation is y = -x - 4. To determine whether its graph passes through the first quadrant, we need to assess the values for x and y. In the first quadrant, both x and y values are positive.
If we substitute any positive value for x into the equation, we will obtain a negative value for y. Therefore, the graph does not pass through the first quadrant. Hence, the correct answer is option A.
The list shows the scores made be each member of Jaime's discussion group on the last test. 69 79 62 93 73 81 73 78 Which box-and-whiskers plot correctly displays the information? f Box-and-whiskers plot G g Box-and-whiskers plot J h Box-and-whiskers plot F j Box-and-whiskers plot H
Final answer:
To choose the correct box-and-whiskers plot for Jaime's discussion group scores, we must calculate the five key statistics and match them with a plot displaying those exact values, factoring in the majority of scores in the 70-89 range.
Explanation:
To determine which box-and-whiskers plot correctly displays Jaime's discussion group scores, we need to calculate five key statistics: the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and the maximum. These statistics help us create an accurate box plot representation of the dataset.
First, we organize the scores in ascending order: 62, 69, 73, 73, 78, 79, 81, 93. From here, we can identify the minimum (62) and maximum (93) scores directly. The median score will be the average of the fourth and fifth scores since we have an even number of observations, which is (73+73)/2 = 73. The lower quartile (Q1) is the median of the lower half of the data, which would be (69+73)/2 = 71. The upper quartile (Q3) is the median of the upper half of the data, which is (79+81)/2 = 80.
Now that we have all the necessary statistics, we can select the box plot that matches these values. Jaime's scores are mostly within the 70-89 range, reflecting a majority of C and B grades, with a few scores in the 60-69 and 90-100 ranges, which correspond to D/F and A ranges respectively. The correct box-and-whiskers plot will show a box ranging from Q1 (71) to Q3 (80), a median line at 73, a whisker extending to the minimum score of 62, and another whisker extending to the maximum score of 93.
Solve for x (Round to the nearest hundredth)
The table shows summary statistics for guests' ages at two parties.
Party Median age (years) Range (years)
1 17 27
2 19 20
Which conclusion is true?
A. A typical guest at Party 1 was younger than a typical guest at Party 2, and guests' ages were more variable at Party 1 than at Party 2.
B. A typical guest at Party 1 was younger than a typical guest at Party 2, and guests' ages were less variable at Party 1 than at Party 2.
C. A typical guest at Party 1 was older than a typical guest at Party 2, and guests' ages were more variable at Party 1 than at Party 2.
D. A typical guest at Party 1 was older than a typical guest at Party 2, and guests' ages were less variable at Party 1 than at Party 2.
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The number of wild flowers growing each year in a meadow is modeled by the function f(x).
f(x)=[tex] \frac{1000}{1+9e^{-0.4x} } [/tex]
Which statements are true about the population of wild flowers?
Select each correct answer.
A. Initially there were 100 wild flowers growing in the meadow.
B. 42 more wildflowers will grow in the 11th year than in the 10th year.
C. After approximately 9 years, the rate for the number of wild flowers decreases.
D. In the 15th year, there will be 1050 wild flowers in the meadow.
30 deciliters he already has 1 liter.How many liters of milk will he need to buy?
What is the solution to this system of equations?
2/3x + y = 6
-2/3x - y = 2
A. (1, -1)
B. (0, 8)
C. infinitely many solutions
D. no solution
When the given system of equations is added together, it simplifies to '0=8', which is a contradiction. Therefore, the system of equations has no solution.
Explanation:You can simply add the two equations together. Adding the two equations eliminates the variables x and y:
(2/3x - 2/3x) + (y - y) = 6 + 2
This simplifies to 0 = 8, which is a contradiction. Therefore, this system of equations has no solution. That means the correct answer is D. 'No solution'.
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Find the diameter of a sphere with the volume 7776pi in^3
Answer:
The diameter is 36 inches
Step-by-step explanation:
The volume of a sphere is
[tex] \frac{4}{3} \pi {r}^{3} [/tex]
The given sphere has volume
[tex]7776\pi {in}^{3} [/tex]
We can now equate the formula to the given volume and solve for r.
[tex]\frac{4}{3} \pi {r}^{3} = 7776\pi[/tex]
[tex] {r}^{3}= 7776\pi \times \frac{3}{4\pi} [/tex]
[tex] {r}^{3} = 5832[/tex]
[tex]r = \sqrt[3]{5832} [/tex]
[tex]r = 18[/tex]
The diameter of the sphere is twice the radius.
Hence
[tex]diameter = 2 \times 18 = 36in[/tex]
I NEED HELP ASAP
Use Euler’s Formula to find the missing number ?
Faces:21
Vertices:14
Edges:?
A.34 B.32 C.33 D.36
two joggers run 8 miles north and then 5 miles west. what is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point? round to the nearest tenths place
The shortest distance they travel to return to starting point is 9.43 miles.
Since, two joggers run 8 miles north and then 5 miles west.
According to question , a right triangle is formed. and hypotenuse of right triangle represent the shortest distance between starting point to final point.
Apply Pythagoras theorem,
Shortest distance, [tex]=\sqrt{8^{2}+5^{2} } =\sqrt{64+25}=\sqrt{89}=9.43miles[/tex]
Thus, They travel 9.43 miles to return to their starting point.
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Ken's cafe serves hot cocoa.each serving has 9 grams of chocolate.how many grams of chocolate are in 8 servings of hot cocoa?
Please need some help on this
There are 453.592 grams in one pound . A semi slick , Kevlar tire weighs about 520 grams . What is the tires weighs in pounds ?
Ricardo just received a shipment of 50 tool sheds for his garden supply store. Each shed costs him $40. Which of the following could Ricardo use to find the total amount he will pay for the tool sheds?
Ricardo will calculate the total amount he will pay for the 50 tool sheds by multiplying the quantity (50 sheds) by the cost per shed ($40), which equals $2,000.
To calculate the total amount Ricardo will pay for the 50 tool sheds he received, he needs to multiply the number of sheds by the cost per shed. Since each shed costs him $40, the calculation to find the total cost is as follows:
Multiply the quantity of tool sheds by the cost per shed: 50 sheds imes $40 per shed.
Calculate the product to find the total cost: 50 imes $40 = $2,000.
Therefore, Ricardo will pay a total of $2,000 for the 50 tool sheds.
4.05E+9 In scientific notation ?
4.05E+9 in scientific notation is 4.05 x 10^9.
4.05E+9 in scientific notation is 4.05 × 109. When a number is given in scientific notation, the coefficient is multiplied by 10 raised to the power of the exponent.
Sarah has grades of 98 and 98 on her first two tests. If she wants an average of at least 80 after her third test, what score must she make on that test
Sarah must score at least 44 on her third test in order to have an average of at least 80.
Explanation:To find out what score Sarah must make on her third test in order to have an average of at least 80, we can set up an equation. The average of her three test scores can be calculated by adding up her scores and dividing by 3:
Average = (98 + 98 + x) / 3
We want the average to be at least 80, so we can solve the equation for x:
(98 + 98 + x) / 3 ≥ 80
Simplifying the equation, we get:
196 + x ≥ 240
Subtracting 196 from both sides, we have:
x ≥ 44
Therefore, Sarah must score at least 44 on her third test in order to have an average of at least 80.
Sarah needs to score at least a 44 on her third test to have an average of at least 80 across her three test scores.
Explanation:Sarah has grades of 98 and 98 on her first two tests and wants to have an average of at least 80 after her third test. To calculate the minimum score Sarah must make on the third test to achieve her goal, we use the formula for the average of three numbers, which is (test1 + test2 + test3) / 3. In Sarah's case, the average after three tests should be at least 80.
Let's represent the third test score as 'x'. Thus, the equation to find 'x' becomes:
(98 + 98 + x) / 3 ≥ 80
Combining the scores of the first two tests gives us:
(196 + x) / 3 ≥ 80
By multiplying both sides by 3 to eliminate the denominator, we have:
196 + x ≥ 240
Subtract 196 from both sides to solve for x:
x ≥ 240 - 196
x ≥ 44
Therefore, Sarah must score at least a 44 on her third test to achieve an average of 80.
find the limit of (sqrt(x+5)-4)/(x-11) as x approaches 11
[tex] \lim\limits_{x\to11}\dfrac{\sqrt{x+5}-4}{x-11}=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5}-4)(\sqrt{x+5}+4)}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{(\sqrt{x+5})^2-4^2}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{x+5-16}{(x-11)(\sqrt{x+5}+4)}\\\\=\lim\limits_{x\to11}\dfrac{x-11}{(x-11)(\sqrt{x+5}+4)}=\lim\limits_{x\to11}\dfrac{1}{\sqrt{x+5}+4}=\dfrac{1}{\sqrt{11+5}+4}\\\\=\dfrac{1}{\sqrt{16}+4}=\dfrac{1}{4+4}=\dfrac{1}{8}\\\\Answer:\ d.\ \dfrac{1}{8} [/tex]
Your friend Zoe is very earnest about the benefits of her special diet. She believes that having kale for breakfast every day will lower your cholesterol.
4a. What's the best method for testing Zoe's claim: a survey, an observational study, or an experiment? Give at least one reason to support your answer. (4 points)
4b. Describe how you would set up a test to determine how much truth there is to Zoe's claims. In particular, what steps would you take to make sure the results were unbiased and valid?
which types of triangles can be formed by taking the cross section of a cube
Monica measures 91 milliliters of water into 9 tiny beakers. she measures an equal amount of water into the first 8 beakers. she pours the remaining water into the ninth beaker.It measures 19 milliliters. how many milliliters of water are in each of the first eight beakers
Can someone please help me with this.
convert: 7 tons 500 lb to lb
Final answer:
7 tons and 500 pounds equals 14,500 pounds, which is calculated by converting tons to pounds and adding the additional pounds.
Explanation:
To convert 7 tons and 500 pounds to pounds only, follow these two steps:
Convert tons to pounds. Since 1 ton is equal to 2,000 pounds, you multiply the number of tons by 2,000. For 7 tons, it would be 7 × 2,000 = 14,000 pounds.
Add the additional pounds to the converted weight. So, you would add 500 pounds to 14,000 pounds, resulting in 14,500 pounds.
Therefore, 7 tons and 500 pounds is equivalent to 14,500 pounds.
The diameter of a DVD is 12 centimeters. The hole in the center of a DVD has a diameter of 1.5 centimeters. Find the area of the DVD. Round to the nearest hundredth if necessary.
The area of the circular DVD is given by A = 111.33 cm²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the area of the circular DVD be A
Let the diameter of the DVD = 12 cm
So , the radius of the DVD = 6 cm
Now , the diameter of the hole = 1.5 cm
So , the radius of the hole = 0.75 cm
And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]
On simplifying , we get
The area of circular DVD is A = π ( 36 - 0.5625 )
The area of circular DVD is A = π ( 35.4375 )
The area of circular DVD is A = 111.33 cm²
Hence , the area of the circular DVD is 111.33 cm²
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Roy borrows $42,000 to purchase a new truck. How much will Roy need to pay in all if the interest is compounded annually at 3.5% for 10 years? (5 points) $43,125.00 $63,624.00 $59,245.15 $51,709.00
-8r - 2 + 7r= -9
solve the equation. then check the solution
Write the standard form of the equation of the circle with the radius of 12 and center at the origin.
The standard form of the equation of the circle with the radius of 12 and center at the origin is,
⇒ x² + y² = 144
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
the radius of circle is, 12 and center at the origin.
Now, We know that;
Standard form of circle with center origin and radius r is,
⇒ x² + y² = r²
Here, r = 12
Hence, The standard form of the equation of the circle with the radius of 12 and center at the origin is,
⇒ x² + y² = 12²
⇒ x² + y² = 144
Thus, The standard form of the equation of the circle with the radius of 12 and center at the origin is,
⇒ x² + y² = 144
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Plz help identify the slope of 8x-3y=12 without graphing the line.
Match the trinomials with their factors. Tiles a2 + a − 20 a2 − 9a + 20 a2 − 8a − 20 a2 − 12a + 20 a2 − 19a − 20 Pairs Factors Trinomials (a − 4)(a − 5) arrowBoth (a − 10)(a − 2) arrowBoth (a − 4)(a + 5) arrowBoth (a − 10)(a + 2) arrowBoth
Trinomial [tex]a^2 + a - 20[/tex] with factors (a + 5)(a - 4)
Trinomial [tex]a^2 - 9a + 20[/tex] with factors (a - 4)(a - 5)
Trinomial [tex]a^2 - 8a - 20[/tex] with factors (a - 10)(a + 2)
Trinomial [tex]a^2 - 12a + 20[/tex] with factors (a - 10)(a - 2)
To match the trinomials with their factors, we can factor each trinomial and compare the factors given:
1. Factorizing trinomial [tex]a^2 + a - 20:[/tex]
The factors are (a + 5)(a - 4).
This matches with the pair (a - 4)(a + 5).
2. Factorizing trinomial [tex]a^2 - 9a + 20:[/tex]
The factors are (a - 4)(a - 5).
This matches with the pair (a - 4)(a - 5).
3. Factorizing trinomial [tex]a^2 - 8a - 20[/tex]:
The factors are (a - 10)(a + 2).
This matches with the pair (a - 10)(a + 2).
4. Factorizing trinomial [tex]a^2 - 12a + 20:[/tex]
The factors are (a - 10)(a - 2).
This matches with the pair (a - 10)(a - 2).
Therefore, the correct matches are:
- Trinomial [tex]a^2 + a - 20[/tex] with factors (a + 5)(a - 4)
- Trinomial [tex]a^2 - 9a + 20[/tex] with factors (a - 4)(a - 5)
- Trinomial [tex]a^2 - 8a - 20[/tex] with factors (a - 10)(a + 2)
- Trinomial [tex]a^2 - 12a + 20[/tex] with factors (a - 10)(a - 2)
30 POINTS - The tables below represent the profits earned by a merchandiser from four new consignments of t-shirts. Each consignment contained t-shirts of five different sizes. If we were to plot each of the t-shirt sizes and the profit earned on each new size, we would get a different graph for each consignment. Almost all the graphs showed some association between the two variables, except one consignment, which showed no association. Which of the following consignments shows no association?