Sara wrote 524 words in her journal. Then she crossed out 56 words and added 95 new words. How many words are written in her journal now?
Olive wants to invite friends over for some ice cream. She has a total of 8 pints of ice cream in her freezer. If she splits each pint into 1/2 pint servings, how many servings of ice cream will olive have?
Solve the equation x^16 – 2x^15 – x^14 + 4x^13 – x^12 – 2x^11 + x^10 = 0 in the real number system.
a) x = 0 with multiplicity 10, x = –1 with multiplicity 4, x = 1 with multiplicity 2
b) x = 0 with multiplicity 10, x = –1 with multiplicity 3, x = 1 with multiplicity 3
c) x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4
d) x = –1 with multiplicity 2, x = 1 with multiplicity 4
Answer:
C:x = 0 with multiplicity 10, x = –1 with multiplicity 2, x = 1 with multiplicity 4
Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.) Tiles area: 221.5584 square units area: 78.5 square units area: 452.16 square units area: 36.2984 square units area: 314 square units area: 886.2336 square units Pairs radius: 12 units arrowBoth diameter: 16.8 units arrowBoth radius: 3.4 units arrowBoth diameter: 10 units arrowBoth
For what interval is the function f(x) = (20 + \sqrt{x}) / (\sqrt{20 + x}) continuous?
Write a number sentence that compares 3/5 and 5/6
3.1 Q15
An athlete whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an angle of 70°, it's height, f(x), in feet, can be modeled by:
[tex]f(x)=-0.06x^2 + 2.7x + 5.9[/tex]
where x is the shot's horizontal distance, in feet, from its point of release.
What is the maximum height of the shot and how far from it's point of release does this occur?
The maximum height reached by the shot is 36.375 feet. This occurs at a horizontal distance of 22.5 feet from its point of release.
Explanation:This is a question about the maximum height of a shot put. The equation presented here is a quadratic function, and it has the form of a parabola. The maximum value of a parabola that opens downwards (as in this case, where the coefficient of x2 is negative) is given at its vertex.
To find the 'x' coordinate of the vertex, use the formula -b/2a, where 'a' is the coefficient of x2 and 'b' is the coefficient of 'x'. In this case, 'a' is -0.06, and 'b' is 2.7. -b/2a = -(2.7)/(2*-0.06) equals 22.5 feet. This is the horizontal distance from the point of release where the shot reaches the maximum height. To find the maximum height, substitute the value of 'x' into the equation, f(22.5) = -0.06*(22.5)2 + 2.7*22.5 + 5.9. This gives the maximum height as 36.375 feet.Learn more about Maximum Height of Shot here:
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Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are on located on the same side of zero on a number line. The opposite of the opposite of −12 is −12 . The opposite of −12 is −112 . −12 and its opposite are located the same distance from zero on a number line.
there's more than 1 answer
The true statements about the opposite of -12 are that the opposite of the opposite of -12 is -12 and -12 and its opposite are located the same distance from zero on a number line. The opposite of -12 is +12.
Explanation:In mathematics, the opposite of a number is also called its additive inverse, which is the number that, when added to the original number, will result in zero. −12 and its opposite, +12, are indeed located on opposite sides of zero on a number line, not on the same side. The second statement is true, the opposite of the opposite of −12 is indeed −12. The third statement is incorrect, the opposite of −12 is +12, not −112. The fourth statement is also true, −12 and its opposite are both 12 units away from zero on a number line, so they're at the same distance from zero.
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A chord of a circle is a line segment connecting any point on the circle to the center of the circle.
Answer:
FALSE
Step-by-step explanation:
A chord of a circle is a line segment that connects two points on the circle.
Answer:
FALSE
Step-by-step explanation:
what is the sum of the rational expressions below? 2x-1/7x + x/x-2
a. 9x^2-5x+2/7x^2-2
b. 9x^2-5x+2/7x^2-14x
c. 3x-1/8x-2
d. 2x^2-5x+2/7x^2-14x
Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.
Answer:
Step-by-step explanation:
Answer and step-by-step explanation:
Sylvia's expression is h+0.05h.
The variable h represents the cost of the hat.
0.05 represents the 5% sales tax; 5% = 5/100 = 0.05.
0.05h represents the amount of tax paid on the hat. To find a percent of a number, we multiply the decimal form of the percent by the original amount.
The total cost is given by h+0.05h.
Jin's expression is 1.05h.
The variable h represents the cost of the hat.
1.05 represents 100% of the cost of the hat plus the additional 5% tax; 100+5 = 105%; 105% = 105/100 = 1.05.
Together the total cost is given by 1.05h.
convert 3(3.14)/8 radians to degrees
True or False 68oz < 4lb 6oz
Answer:true!!!
Step-by-step explanation:
If a student scored 82 points on a test where the mean score was 78.2 and the standard deviation was 6.7. the student's z score is .
find the values of x and y in the following equation. (x + yi) + (4 + 9) = 9 -4i
In this question we solve the given complex number equation. By comparing real and complex components on both sides of the equation, we find the values satisfying the equation are x = 5 and y=-13.
Explanation:In this complex number equation, we must solve for x and y: (x + yi) + (4 + 9) = 9 -4i. Begin by simplifying the left side of the equation, to give (x + 4 + yi +9i) = 9 - 4i. This further simplifies to (x + 4) + (y + 9)i = 9 -4i.
Now we can see that the real component of the equation (x + 4) must equal the real component on the other side of the equation (9), and the complex component of the equation (y + 9)i must equal the complex component -4i. Setting these equal gives x + 4 = 9 and y + 9 = -4.
Solving these gives x = 5 and y = -13, which are the values for x and y satisfying the equation.
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Melissa bought a cake that cost $75. the sales-tax rate is 10 percent. what is the total amount she paid for the cake
Answer:
The total amount that Melissa paid for the cake is $82.5
Step-by-step explanation:
we know that
The total amount that Melissa paid for the cake is equal to the cost of the cake plus the sales tax
we have that
the cost is equal to $75
Find the sales tax
The sales tax is 10%, therefore find the 10% of the cost of the cake
10%=10/100=0.10
so
(0.10)*$75=$7.5
Adds the cost and the sales tax
$75+$7.5=$82.5
64 is 4 times the difference between Sarah's age a and 44 assume Sarah is older than 44 write an equation to determine Sarah's age a
Answer:
Sarah's age is 60.
Step-by-step explanation:
We have that Sarah's age is a.
The problem states that 64 is 4 times the difference between Sarah's age a and 44.
So
[tex]a - 44 = \frac{64}{4}[/tex]
[tex]a - 44 = 16[/tex]
[tex]a = 44 + 16[/tex]
[tex]a = 60[/tex].
Sarah's age is 60.
The set of points (2, 3), (9, 3), (9, –2), and (2, –2) identifies the vertices of a quadrilateral. Which is the most specific description to tell which figure the points form?
A parallelogram
B square
C rectangle
D trapezoid
Answer:
C rectangle
Step-by-step explanation:
All the coordinates of the setpoint are (x,y) so, you need to draw the axis and you'll found a rectangle (attached)
It is not a square because its side and height are not equal.
It is not a parallelogram because there are no diagonals.
It is not a trapezoid because it has parallels sides.
It's a rectangle because it has two pairs or parallels, one longer than the other.
Solve the following word problem. A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?
______ miles
Distance from Town X to Town Y = 100 miles
Distance = Speed x Time
Speed while going = 50 mph , Speed while returning = 40 mph
Let the time taken while going = t hours
So, the time taken while returning = t + 0.5 hours
Distance while going = Distance while coming backSo, 50 t = 40 ( t + 0.5)
50 t = 40x + 20
50 t - 40 t = 10x = 20
10 t = 20
t = 20 / 10 = 2
Hence, distance = 50 t = 40 ( t + 0.5 )
= 50 x 2 ; or 40 x 2.5 = 100
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The distance from Town X to Town Y is 180 miles. This is determined by setting up and solving an equation based on the given speeds and time difference.
Explanation:The subject of this question is Mathematics, specifically it is a problem in a genre called distance, speed, time problems. Let's denote the distance from Town X to Town Y as 'd' miles. The man covers this distance twice - once going and once coming back. The time he takes to travel from X to Y is d/50 and to travel back from Y to X is d/40.
So, the actual total time he spends travelling is (d/50 + d/40) hours. If he made the round trip at an average speed of 45 mph, he would take (2d/45) hours (distance = speed x time). Given that the actual journey took a 1/2 hour longer than this, we can create the following equation:
(d/50 + d/40) = 2d/45 + 1/2.
Solving this equation for 'd', we get d = 180 miles. So, the answer is that the distance from Town X to Town Y is 180 miles.
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Solve 12 = x/4 algebraically. Then, check your answer.
A cake recipe suggests a cooking temperature of 325 °F if the batter is less than one inch thick and 350 °F if the batter is more than one inch thick. If the cake batter has a volume of 110 in3 and your cake pan is 9 inches by 11 inches, what does the oven need to be set at if the oven temperature settings are in degrees Celsius? (round to nearest whole number) A) 140 °C B) 163 °C C) 177 °C D) 190 °C
Answer C
the shape of cake pan is usually cuboid
volume of cuboid = length * breadth * height
110 = 9 *11 * height
height = 10/9 = 1.11 inches
so, the batter is more than 1 inch thick,
the temperature required is 350 degree F or 177 degree C
The system of equations is graphed on the coordinate plane. y=−12x−1y=14x−4 A graph with a blue line passing through coordinates (0, -4) and (4, -3) and a red line passing through coordinates (0, -1) and (4, -3). Enter the coordinates of the solution to the system of equations in the boxes. ( , )
please translate 2 minus the product of a number and 9 is 20.
The statement '2 minus the product of a number and 9 is 20' translates to the equation 2 - 9x = 20. Solving for x, we find the solution x = -2, meaning the number in question is -2.
The student is asking to translate the phrase '2 minus the product of a number and 9 is 20' into a mathematical equation. The 'product of a number and 9' can be represented as '9x' where 'x' is the unknown number. Therefore, translating the entire phrase, we end up with the equation: 2 - 9x = 20.
To solve for 'x', we first bring '9x' to the other side of the equation by adding '9x' to both sides, resulting in 2 = 9x + 20. Subsequently, we subtract 20 from both sides, yielding -18 = 9x, and then we divide both sides by 9 to find the value of 'x'. So, x = -18 / 9, which simplifies to x = -2.
The solution for the equation is x = -2, which means the number we were looking for is -2.
gabriel made 4 small meatloaves. he cut each meatloaf into fourths. how many 1/4 size pieces of meatloaf does gabriel have
The area of circular garden is 530.66 feet2. What is the circumference of the garden? (Use 3.14 for .
what is the square root of 64 multiplied by 72 divided by the sum of 43 plus 0
From the sample space sequals={1, 2, 3, 4,..., 15} a single number is to be selected at random. given event a, that the selected number is even, and event b, that the selected number is a multiple of 4, find p(upper a vertial line upper ba∣b).
The probability of randomly selecting an even number given that the number is a multiple of 4, or p(A|B), is 1.
Explanation:The question is asking for the conditional probability p(A|B), meaning the probability of event A (number is even) given that event B (number is a multiple of 4) has already occurred. In this sample space, there are 8 even numbers {2, 4, 6, 8, 10, 12, 14, 16} and 4 multiples of 4 {4, 8, 12, 16}. Therefore, the probability of picking an even number out of the ones that are multiples of 4 is as follows:
First, determine the probability of event A within event B by dividing the number of favorable outcomes (even numbers and multiples of 4) by the total outcomes of event B. In this case, all multiples of 4 are even numbers, so there are 4 favorable outcomes.
Calculating p(A|B): Number of instances where A and B occur together / Number of instances where B occurs = 4 / 4 = 1
Therefore, the probability of randomly selecting an even number given that the number is a multiple of 4, p(A|B), is 1.
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A tree on a hillside casts a shadow c = 235 ft down the hill. if the angle of inclination of the hillside is b = 16° to the horizontal and the angle of elevation of the sun is a = 46°, find the height of the tree. (round your answer to the nearest foot.)
Final answer:
By using the tangent function with the effective angle formed by the difference between the sun's elevation and the hill's incline, and the length of the shadow, we calculate the height of the tree to be approximately 136 feet.
Explanation:
To find the height of a tree on a hillside, we utilize the given angles and the length of the shadow it casts. The shadow is cast down the hill (c = 235 ft) with the hill inclining at an angle of 16° to the horizontal (b) and the sun's angle of elevation at 46° (a). To solve this, we can use trigonometry, specifically the concept of similar triangles and the tangent function, which relates the angle to the ratio of the opposite side over the adjacent side in a right triangle.
First, we find the effective angle Θ the sun's rays make with the hillside, which is the difference between the sun's elevation angle and the hill's inclination angle: Θ = 46° - 16° = 30°. Then, using the tangent function which involves the height of the tree (h) and the length of the shadow (c), we set up the equation tan(Θ) = h / c. Substituting the values gives tan(30°) = h / 235 ft.
Next, we solve for h: h = 235 ft x tan(30°). Calculating this, we find h is approximately 135.7 ft. Therefore, rounding to the nearest foot, the height of the tree is 136 feet.
There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.
A hurricane has a large eye of about 80 miles. How many kilometers wide is the eye?
It is given that a hurricane has a large eye of about 80 miles.
We have to determine about how many kilometers wide is the eye.
Since 1 mile = 1.6 kilometers (approximately)
To convert the unit 'mile' into 'kilometer' ,
we have to multiply the given number by '1.6'.
So, 80 miles = [tex] 80 \times 1.6 = 128 [/tex] kilometers.
So, the hurricane eye is about 128 kilometers wide.
Final answer:
To convert 80 miles to kilometers, multiply by the conversion factor of 1.60934, resulting in an eye of the hurricane that is approximately 128.75 kilometers wide.
Explanation:
To convert the size of a hurricane's eye from miles to kilometers, we use the conversion factor that 1 mile is approximately equal to 1.60934 kilometers. If a hurricane has an eye that is about 80 miles wide, we need to multiply this distance by the conversion factor to obtain the width in kilometers.
Step-by-step Conversion:
Identify the width of the hurricane's eye in miles: 80 miles.
Use the conversion factor: 1 mile = 1.60934 kilometers.
Multiply the width in miles by the conversion factor to get the width in kilometers: 80 miles * 1.60934 km/mile = 128.7472 kilometers.
Therefore, the eye of the hurricane is approximately 128.75 kilometers wide.