The probability that one number is twice the other number when two different cards are chosen at random is 1/49.
Explanation:To find the probability that one number is twice the other number when two different cards are chosen at random from a set of 50 cards numbered from 1 to 50, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes occur when one card is twice the value of the other card. Let's consider the smaller number as 'x'. In that case, the larger number would be '2x'. We can see that 'x' can take any value from 1 to 25, since the larger number '2x' should be less than or equal to 50.
So, the number of favorable outcomes is 25. The total number of possible outcomes is the number of ways to choose 2 cards out of 50, which is given by the combination formula: C(50, 2) = 50! / (2! * (50-2)!), which simplifies to 50 * 49 / 2 = 1225.
Therefore, the probability is given by the ratio of the favorable outcomes to the total number of possible outcomes: 25/1225 = 1/49.
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Find the measure of ∠AED
Castel made a trip to the ferry office and back. On the trip there he traveled 60 km/h and on the return trip he went 45 km/h. How long did the trip there take if the return trip took four hours?
Which number line represents the graph of x ≤ 0?
Answer:
first one
Step-by-step explanation:
The number line represents the graph of x ≤ 0 is number line (b)
How to determine the number line?The inequality expression is given as:
x ≤ 0
The inequality symbol ≤ means that:
The number line starts at 0The arrow faces the leftThe circle at 0 is a closed circleHence, the number line represents the graph of x ≤ 0 is number line (b)
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A plumber charges $70 per hour plus $40 dollars for the call. What does he charge for 4 hours of work
In how many games did the team score at least 70 points?
Answer: the answer is 5
Step-by-step explanation:
b
Raise to the power:
(–0.2xy)4
What are the missing angle measures in triangle ABC?
a.1.4° and 88.6°
b.18.6° and 71.4°
c.35.5° and 54.5°
d.44.4° and 45.6°
angle a = arctan(5/7) = 35.5
angle b = arctan(7/5) = 54.5
Answer is C
Answer:
(C)35.5° and 54.5°
Step-by-step explanation:
It is given that ABC is a right angled triangle which is right angled at C and AC=7 inches and CB=5 inches.
Now, using the trigonometry, we have
From ΔABC, we have
[tex]\frac{BC}{AC}=tanA[/tex]
[tex]\frac{5}{7}=tanA[/tex]
[tex]0.714=tanA[/tex]
[tex]A=tan^{-1}(0.714)[/tex]
[tex]A=35.5^{\circ}[/tex]
Again, from ΔABC, we have
[tex]\frac{AC}{BC}=tanB[/tex]
[tex]\frac{7}{5}=tanB[/tex]
[tex]1.4=tanB[/tex]
[tex]B=tan^{-1}(1.4)[/tex]
[tex]B=54.5^{\circ}[/tex]
Therefore, the measure of missing angles in triangle ABC are 35.5° and 54.5°respectively.
Thus, option C is correct.
Which phrase describes an unknown or changeable quantity?
A cotton candy vendor has 11 cones of blue cotton candy to sell. if the blue cotton candy is 25% of the total number of cones, how many total cotton candy cones does he have
Alison wants to construct the perpendicular bisector of MN¯¯¯¯¯¯¯. What should Alison do for her first step? A.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is equal to 1/2MN . B.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN. C.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is less than 1/2MN. D.) Use the straightedge to draw a line that intersects MN¯¯¯¯¯¯¯ at a point between M and N.
Answer:
Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN.
Step-by-step explanation:
The site told me that correct answer was B., so it was greater than.
NEED HELP! Thanks!
Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the other train travels at 80 mph.
How much time passes until the trains are 600 mi apart?
Enter your answer in the box.
Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
What is the length of one of the diagonals of the rectangle?
Enter an expression in the box for the length of the diagonal.
The length of a line with known end point coordinates is given by Pythagoras's theorem
The expression for the length of the diagonal [tex]\overline{PR}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]
The expression for the length of the diagonal [tex]\overline{QS}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]
Reason:
The given coordinates of the vertices are; P(0, b), Q(a, b), R(a, 0), and S(0, 0)
Diagonals of the rectangle are segments; [tex]\overline{PR}[/tex], and [tex]\overline{QS}[/tex]The lengths of the diagonals are given by the equation for finding the length, l, of a line given the coordinates which is [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where:
(x₁, y₁) = P(0, b), and (x₂, y₂) = R(a, 0), we get;
[tex]Length \ of \ diagonal \ segment \ \overline{PR} = \sqrt{\left (0-b \right )^{2}+\left (a-0 \right )^{2}} = \sqrt{b^2 + a^2}[/tex]Where:
(x₁, y₁) = Q(a, b), and (x₂, y₂) = S(0, 0), we get;
[tex]Length \ of \ diagonal \ segment \ \overline{QS} = \sqrt{\left (0-b \right )^{2}+\left (0-a \right )^{2}} = \sqrt{b^2 + a^2}[/tex]Therefore,
The expression for the length of the diagonal is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]Learn more here:
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What is the japanese poetry of a pattern of 5 7-5 syllables?
What does .9999 rounded to the thousandths?
Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown.
What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?
In a parallelogram, all angles are congruent
In a parallelogram, consecutive angles are congruent.
In a parallelogram, consecutive angles are supplementary.
In a parallelogram, all angles are supplementary.
Solution-
1st statement- In a parallelogram, all angles are congruent.
If all the angels are congruent then all angles will be 90° (as summation of all the angles are 360° and 360/4= 90°), then it will be either a rectangle or a square, not a parallelogram.
2nd statement- In a parallelogram, consecutive angles are congruent.
If consecutive angles are congruent, then it will be rectangle or a square, not a parallelogram. In a parallelogram, opposite angles are congruent not consecutive angles.
4th statement- In a parallelogram, all angles are supplementary.
In a parallelogram, all the consecutive angles are supplementary or summation of measurements consecutive angles is 180°, not all the angels are supplementary, because opposite angles can't be supplementary.
3rd statement- In a parallelogram, consecutive angles are supplementary.
This is the reasonable conjecture for a parallelogram, because always the summation of measurement of consecutive angles are 180°.
How would you graph and solve this ?? Plz help! Open to see image.
what is the advantage of multiplying both sides of the equation by the least common multiple of the denominators in the first step?
for a different pizza dough recipe, the equation f=2.5w represents the number of cups of flour, f, that you need for w cups of water. what is the constant of proportionality? explain what it means in this context.
For any direct variation, the equation is of the form y = kx, where k is the constant of proportionality.
Given the equation: f = 2.5wThe constant of proportionality is 2.5.
This means that the ration of the cups of flour to the cups of water used in the recipe is 2.5
Final answer:
The constant of proportionality in the equation f=2.5w is 2.5, representing the ratio of cups of flour to cups of water for the recipe.
Explanation:
Proportionality Constant:
The constant of proportionality in the equation f=2.5w is 2.5. In this context, the constant of proportionality represents the ratio of cups of flour to cups of water needed for the pizza dough recipe.
Explanation:
The constant 2.5 indicates that for every cup of water (w), you will need 2.5 cups of flour (f) in the pizza dough recipe.
The length of a rectangular jewelry box is 3 in. more than twice the width. the perimeter is 36 in. find the length and the width.
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15
we have
[tex]x<9[/tex] ------> inequality A
The solution of the inequality A is the interval--------> (-∞,9)
All real numbers less than [tex]9[/tex]
[tex]x\geq14[/tex] -----> inequality B
The solution of the inequality B is the interval--------> [14,∞)
All real numbers greater than or equal to [tex]14[/tex]
The solution Inequality A or Inequality B is equal to
Solution A+Solution B
(-∞,9)U[14,∞)
The solution of the compound system of inequalities must satisfy inequality A or inequality B
we're going to verify every case
case A) [tex]\$8[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]8<9[/tex] -------> is true
Therefore
[tex]\$8[/tex] is a possible value for x
You don't need to check for inequality B
case B) [tex]\$9[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]9<9[/tex] -------> is not true
Verify inequality B
[tex]9\geq14[/tex] ------> is not true
Therefore
[tex]\$9[/tex] is not a possible value for x
case C) [tex]\$11[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]11<9[/tex] -------> is not true
Verify inequality B
[tex]11\geq14[/tex] ------> is not true
Therefore
[tex]\$11[/tex] is not a possible value for x
case D) [tex]\$13[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]13<9[/tex] -------> is not true
Verify inequality B
[tex]13\geq14[/tex] ------> is not true
Therefore
[tex]\$13[/tex] is not a possible value for x
case E) [tex]\$14[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]14<9[/tex] -------> is not true
Verify inequality B
[tex]14\geq14[/tex] ------> is true
Therefore
[tex]\$14[/tex] is a possible value for x
case F) [tex]\$15[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]15<9[/tex] -------> is not true
Verify inequality B
[tex]15\geq14[/tex] ------> is true
Therefore
[tex]\$15[/tex] is a possible value for x
therefore
the answer is
[tex]\$8[/tex]
[tex]\$14[/tex]
[tex]\$15[/tex]
What is solution to the system of equations? Y=5×+2 3×=-y+10
Which equation can be used to find the answer? sharifa spends $51 on the first day of her vacation. this leaves her with $127 to spend during the rest of her vacation. how much money did sharifa bring to spend during her vacation?
a. t = 127 · 2 t = 254 $254
b. t – 51 = 127 t = 178 $178
c. t + 51 = 127 t = 76 $76
d. t = 127 ÷ 2 t = 63.5 $63.5?
Movie tickets for an adult and three children cost $20. an adult's ticket costs $2 more than a child's ticket. find the cost of an adult's ticket.
How do i graph y= 2x
Ms. johnson's class is having a pizza party. if there are 14 students and 7 pizzas cut into 8 slices, what answer choice represents the fraction of one pizza that each student receives?
We are asked about the fraction of pizza each student gets, so the relevant numbers here is only 14 students and 7 pizzas. SO the fraction of pizza each student get is the ratio of the two:
fraction = 7 pizzas / 14 students
fraction = 1 / 2
So each student gets 1/2
Each student receives 4 slices out of 8, or half a pizza, which is represented by the fraction 1/2. There are 56 slices available in total (7 pizzas times 8 slices each), and when that is divided by 14 students, it equals 4 slices per student.
The question asks for the fraction of one pizza that each student receives at a pizza party. Given that there are 14 students and 7 pizzas, each pizza is cut into 8 slices. This information can be used to calculate the total number of slices available and then divide that by the number of students to determine the fraction of a pizza each student gets.
First, we find the total number of slices by multiplying the number of pizzas by the number of slices per pizza:
7 pizzas x 8 slices per pizza = 56 slices
Next, we divide the total number of slices by the number of students to find how many slices each student will receive:
56 slices ÷ 14 students = 4 slices per student
Since each pizza has 8 slices, 4 slices represent half a pizza. Therefore, the fraction of one pizza that each student receives is 1/2.
a mans weekly wage was £336 but now he earns £420. what is the percentage change
A car is traveling at a rate of 50 miles per hour. what is the car's rate in kilometers per hour? how many kilometers will the car travel in 3 hours? in your computations, assume that 1 mile is equal to 1.6 kilometers.
Final answer:
To convert 50 miles per hour to kilometers per hour, multiply by 1.6 to get 80 km/h. In 3 hours, the car will travel 240 kilometers.
Explanation:
The student is asking how to convert a car's speed from miles per hour (mi/h) to kilometers per hour (km/h), and then calculate the distance traveled in kilometers over a period of 3 hours.
Conversion from mi/h to km/h
To convert the car's speed from miles per hour to kilometers per hour, you can use the conversion factor that 1 mile is equal to 1.6 kilometers. Given the car's speed of 50 miles per hour, the calculation would be:
Speed in km/h = Speed in mi/h imes Conversion factor = 50 mi/h imes 1.6 km/mi = 80 km/h.
Distance Traveled in 3 Hours
Now, to compute the distance the car will travel in 3 hours at 80 km/h, use the formula:
Distance = Speed imes Time = 80 km/h imes 3 h = 240 kilometers.
Factor the expression below x^2 -6x+9
Answer:
Factor: [tex](x-3)(x-3)[/tex]
Step-by-step explanation:
Given: [tex]x^2-6x+9[/tex]
Factor the given polynomial. It is quadratic equation.
[tex]\Rightarrow x^2-6x+9[/tex]
Using formula: [tex]a^2-2ab+b^2=(a-b)^2[/tex]
So, first we make given polynomial to perfect square.
[tex]\Rightarrow x^2-2\cdot x\cdot 3+3^2[/tex]
[tex]a\rightarrow x[/tex]
[tex]b\rightarrow 3[/tex]
[tex]\Rightarrow (x-3)^2[/tex]
[tex]\Rightarrow (x-3)(x-3)[/tex]
Hence, The factor of given polynomial is [tex]\Rightarrow (x-3)(x-3)[/tex]
Factorizing the polynomial expression x² - 6x + 9 = (x - 3)²
What is factorization?Factorization is the simplification of an expression into a smaller expression using its factors.
To factor the polynomial expression. x² - 6x + 9, we proceed as follows
Since we have the polynomial expression x² - 6x + 9, we multiply x² by 9 to get x² × 9 = 9x².
Now, we desire to find the factors of 9x² so that the sum of those factors equal - 6x
Thus, we have 9x² = -3x × (-3x)
So, -6x = -3x - 3x
Thus, we replace this with -6x, so
x² - 6x + 9 = x² - 3x - 3x + 9
So, factorizing, we have that
x² - 3x - 3x + 9 = x(x - 3) - 3(x - 3)
= (x - 3)(x - 3)
= (x - 3)²
So, factorizing x² - 18x + 81 = (x - 9)²
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How many 1-cm squares would it take to construct a square that is 3 m on each side?
7.9×10^-6 in standard notation.